TSTP Solution File: SEU734^2 by Lash---1.13

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEU734^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n016.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 17:24:19 EDT 2023

% Result   : Theorem 20.25s 20.70s
% Output   : Proof 20.25s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

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

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

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

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

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

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

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

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

thf(sP2,plain,
    ( sP2
  <=> ! [X1: $i,X2: $i] :
        ( ( in @ X2 @ ( powerset @ X1 ) )
       => ! [X3: $i] :
            ( ( in @ X3 @ ( powerset @ X1 ) )
           => ( in @ ( binintersect @ X2 @ X3 ) @ ( powerset @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( in @ ( binintersect @ eigen__1 @ eigen__2 ) @ ( powerset @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( in @ ( setminus @ eigen__0 @ eigen__1 ) @ ( powerset @ eigen__0 ) )
     => ! [X1: $i] :
          ( ( in @ X1 @ ( powerset @ eigen__0 ) )
         => ( ! [X2: $i] :
                ( ( in @ X2 @ eigen__0 )
               => ( ( in @ X2 @ ( setminus @ eigen__0 @ eigen__1 ) )
                 => ( in @ X2 @ X1 ) ) )
           => ( subset @ ( setminus @ eigen__0 @ eigen__1 ) @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: $i,X2: $i] :
        ( ( in @ X2 @ ( powerset @ X1 ) )
       => ! [X3: $i] :
            ( ( in @ X3 @ ( powerset @ X1 ) )
           => ( ! [X4: $i] :
                  ( ( in @ X4 @ X1 )
                 => ( ( in @ X4 @ X2 )
                   => ( in @ X4 @ X3 ) ) )
             => ( subset @ X2 @ X3 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( in @ ( setminus @ eigen__0 @ ( binintersect @ eigen__1 @ eigen__2 ) ) @ ( powerset @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: $i,X2: $i] :
        ( ( in @ X2 @ ( powerset @ X1 ) )
       => ( in @ ( setminus @ X1 @ X2 ) @ ( powerset @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ( in @ eigen__1 @ ( powerset @ eigen__0 ) )
     => ( in @ ( setminus @ eigen__0 @ eigen__1 ) @ ( powerset @ eigen__0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( ( in @ eigen__1 @ ( powerset @ eigen__0 ) )
     => ! [X1: $i] :
          ( ( in @ X1 @ ( powerset @ eigen__0 ) )
         => ( in @ ( binintersect @ eigen__1 @ X1 ) @ ( powerset @ eigen__0 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ! [X1: $i] :
        ( ( in @ X1 @ ( powerset @ eigen__0 ) )
       => ( in @ ( binintersect @ eigen__1 @ X1 ) @ ( powerset @ eigen__0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ! [X1: $i] :
        ( ( in @ X1 @ ( powerset @ eigen__0 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ ( powerset @ eigen__0 ) )
           => ! [X3: $i] :
                ( ( in @ X3 @ eigen__0 )
               => ( ( in @ X3 @ ( setminus @ eigen__0 @ X1 ) )
                 => ( in @ X3 @ ( setminus @ eigen__0 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( ! [X1: $i] :
          ( ( in @ X1 @ eigen__0 )
         => ( ( in @ X1 @ ( setminus @ eigen__0 @ eigen__1 ) )
           => ( in @ X1 @ ( setminus @ eigen__0 @ ( binintersect @ eigen__1 @ eigen__2 ) ) ) ) )
     => ( subset @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ ( binintersect @ eigen__1 @ eigen__2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( sP1
     => sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ! [X1: $i] :
        ( ( in @ X1 @ eigen__0 )
       => ( ( in @ X1 @ ( setminus @ eigen__0 @ eigen__1 ) )
         => ( in @ X1 @ ( setminus @ eigen__0 @ ( binintersect @ eigen__1 @ eigen__2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ! [X1: $i] :
        ( ( in @ X1 @ ( powerset @ eigen__0 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ ( powerset @ eigen__0 ) )
           => ( ! [X3: $i] :
                  ( ( in @ X3 @ eigen__0 )
                 => ( ( in @ X3 @ X1 )
                   => ( in @ X3 @ X2 ) ) )
             => ( subset @ X1 @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( sP1
     => sP14 ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( in @ eigen__1 @ ( powerset @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ! [X1: $i] :
        ( ( in @ X1 @ ( powerset @ eigen__0 ) )
       => ( in @ ( setminus @ eigen__0 @ X1 ) @ ( powerset @ eigen__0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ( subset @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ ( binintersect @ eigen__1 @ eigen__2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ( sP17
     => ! [X1: $i] :
          ( ( in @ X1 @ ( powerset @ eigen__0 ) )
         => ! [X2: $i] :
              ( ( in @ X2 @ eigen__0 )
             => ( ( in @ X2 @ ( setminus @ eigen__0 @ eigen__1 ) )
               => ( in @ X2 @ ( setminus @ eigen__0 @ ( binintersect @ eigen__1 @ X1 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ! [X1: $i] :
        ( ( in @ X1 @ ( powerset @ eigen__0 ) )
       => ( ! [X2: $i] :
              ( ( in @ X2 @ eigen__0 )
             => ( ( in @ X2 @ ( setminus @ eigen__0 @ eigen__1 ) )
               => ( in @ X2 @ X1 ) ) )
         => ( subset @ ( setminus @ eigen__0 @ eigen__1 ) @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ( in @ ( setminus @ eigen__0 @ eigen__1 ) @ ( powerset @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ( sP3
     => sP6 ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> ! [X1: $i] :
        ( ( in @ X1 @ ( powerset @ eigen__0 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ ( powerset @ eigen__0 ) )
           => ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ eigen__0 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ! [X1: $i] :
        ( ( in @ X1 @ ( powerset @ eigen__0 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ eigen__0 )
           => ( ( in @ X2 @ ( setminus @ eigen__0 @ eigen__1 ) )
             => ( in @ X2 @ ( setminus @ eigen__0 @ ( binintersect @ eigen__1 @ X1 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
    ( sP26
  <=> ! [X1: $i,X2: $i] :
        ( ( in @ X2 @ ( powerset @ X1 ) )
       => ! [X3: $i] :
            ( ( in @ X3 @ ( powerset @ X1 ) )
           => ! [X4: $i] :
                ( ( in @ X4 @ X1 )
               => ( ( in @ X4 @ ( setminus @ X1 @ X2 ) )
                 => ( in @ X4 @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
    ( sP27
  <=> ( sP6
     => sP12 ) ),
    introduced(definition,[new_symbols(definition,[sP27])]) ).

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

thf(def_complementT_lem,definition,
    ( complementT_lem
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( in @ X2 @ ( powerset @ X1 ) )
          @ ( in @ ( setminus @ X1 @ X2 ) @ ( powerset @ X1 ) ) ) ) ) ).

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

thf(def_complementImpComplementIntersect,definition,
    ( complementImpComplementIntersect
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( in @ X2 @ ( powerset @ X1 ) )
          @ ! [X3: $i] :
              ( ^ [X4: $o,X5: $o] :
                  ( X4
                 => X5 )
              @ ( in @ X3 @ ( powerset @ X1 ) )
              @ ! [X4: $i] :
                  ( ^ [X5: $o,X6: $o] :
                      ( X5
                     => X6 )
                  @ ( in @ X4 @ X1 )
                  @ ( ^ [X5: $o,X6: $o] :
                        ( X5
                       => X6 )
                    @ ( in @ X4 @ ( setminus @ X1 @ X2 ) )
                    @ ( in @ X4 @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) ) ) ) ) ) ) ).

thf(complementSubsetComplementIntersect,conjecture,
    ( sP2
   => ( sP7
     => ( sP5
       => ( sP26
         => ! [X1: $i,X2: $i] :
              ( ( in @ X2 @ ( powerset @ X1 ) )
             => ! [X3: $i] :
                  ( ( in @ X3 @ ( powerset @ X1 ) )
                 => ( subset @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) ) ) ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ( sP2
     => ( sP7
       => ( sP5
         => ( sP26
           => ! [X1: $i,X2: $i] :
                ( ( in @ X2 @ ( powerset @ X1 ) )
               => ! [X3: $i] :
                    ( ( in @ X3 @ ( powerset @ X1 ) )
                   => ( subset @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[complementSubsetComplementIntersect]) ).

thf(h1,assumption,
    sP2,
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ( sP7
     => ( sP5
       => ( sP26
         => ! [X1: $i,X2: $i] :
              ( ( in @ X2 @ ( powerset @ X1 ) )
             => ! [X3: $i] :
                  ( ( in @ X3 @ ( powerset @ X1 ) )
                 => ( subset @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    sP7,
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ( sP5
     => ( sP26
       => ! [X1: $i,X2: $i] :
            ( ( in @ X2 @ ( powerset @ X1 ) )
           => ! [X3: $i] :
                ( ( in @ X3 @ ( powerset @ X1 ) )
               => ( subset @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    sP5,
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ ( sP26
     => ! [X1: $i,X2: $i] :
          ( ( in @ X2 @ ( powerset @ X1 ) )
         => ! [X3: $i] :
              ( ( in @ X3 @ ( powerset @ X1 ) )
             => ( subset @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    sP26,
    introduced(assumption,[]) ).

thf(h8,assumption,
    ~ ! [X1: $i,X2: $i] :
        ( ( in @ X2 @ ( powerset @ X1 ) )
       => ! [X3: $i] :
            ( ( in @ X3 @ ( powerset @ X1 ) )
           => ( subset @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ ! [X1: $i] :
        ( ( in @ X1 @ ( powerset @ eigen__0 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ ( powerset @ eigen__0 ) )
           => ( subset @ ( setminus @ eigen__0 @ X1 ) @ ( setminus @ eigen__0 @ ( binintersect @ X1 @ X2 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h10,assumption,
    ~ ( sP17
     => ! [X1: $i] :
          ( ( in @ X1 @ ( powerset @ eigen__0 ) )
         => ( subset @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ ( binintersect @ eigen__1 @ X1 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h11,assumption,
    sP17,
    introduced(assumption,[]) ).

thf(h12,assumption,
    ~ ! [X1: $i] :
        ( ( in @ X1 @ ( powerset @ eigen__0 ) )
       => ( subset @ ( setminus @ eigen__0 @ eigen__1 ) @ ( setminus @ eigen__0 @ ( binintersect @ eigen__1 @ X1 ) ) ) ),
    introduced(assumption,[]) ).

thf(h13,assumption,
    ~ ( sP1
     => sP19 ),
    introduced(assumption,[]) ).

thf(h14,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h15,assumption,
    ~ sP19,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP12
    | ~ sP14
    | sP19 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP13
    | ~ sP1
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP27
    | ~ sP6
    | sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP16
    | ~ sP1
    | sP14 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP10
    | sP13 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP21
    | sP27 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP25
    | sP16 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP9
    | ~ sP17
    | sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP23
    | ~ sP3
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP8
    | ~ sP17
    | sP22 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP4
    | ~ sP22
    | sP21 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP20
    | ~ sP17
    | sP25 ),
    inference(prop_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP24
    | sP9 ),
    inference(all_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP18
    | sP23 ),
    inference(all_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP18
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(16,plain,
    ( ~ sP15
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(17,plain,
    ( ~ sP11
    | sP20 ),
    inference(all_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP2
    | sP24 ),
    inference(all_rule,[status(thm)],]) ).

thf(19,plain,
    ( ~ sP7
    | sP18 ),
    inference(all_rule,[status(thm)],]) ).

thf(20,plain,
    ( ~ sP5
    | sP15 ),
    inference(all_rule,[status(thm)],]) ).

thf(21,plain,
    ( ~ sP26
    | sP11 ),
    inference(all_rule,[status(thm)],]) ).

thf(22,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h14,h15,h13,h11,h12,h10,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,h1,h3,h5,h7,h11,h14,h15]) ).

thf(23,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h13,h11,h12,h10,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h14,h15])],[h13,22,h14,h15]) ).

thf(24,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h11,h12,h10,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__2)],[h12,23,h13]) ).

thf(25,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h10,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h10,24,h11,h12]) ).

thf(26,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__1)],[h9,25,h10]) ).

thf(27,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__0)],[h8,26,h9]) ).

thf(28,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,27,h7,h8]) ).

thf(29,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,28,h5,h6]) ).

thf(30,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,29,h3,h4]) ).

thf(31,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,30,h1,h2]) ).

thf(0,theorem,
    ( sP2
   => ( sP7
     => ( sP5
       => ( sP26
         => ! [X1: $i,X2: $i] :
              ( ( in @ X2 @ ( powerset @ X1 ) )
             => ! [X3: $i] :
                  ( ( in @ X3 @ ( powerset @ X1 ) )
                 => ( subset @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) ) ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[31,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU734^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35  % Computer : n016.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug 24 01:49:53 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 20.25/20.70  % SZS status Theorem
% 20.25/20.70  % Mode: cade22grackle2x798d
% 20.25/20.70  % Steps: 2372
% 20.25/20.70  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------