TSTP Solution File: SEU762^2 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEU762^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n020.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  : 600s
% DateTime : Tue Jul 19 14:02:14 EDT 2022

% Result   : Theorem 0.37s 0.55s
% Output   : Proof 0.39s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

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

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

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

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

thf(ty_eigen__4,type,
    eigen__4: $i ).

thf(ty_eigen__3,type,
    eigen__3: $i ).

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

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

thf(sP1,plain,
    ( sP1
  <=> ( subset @ ( binintersect @ eigen__1 @ eigen__2 ) @ eigen__4 ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( subset @ eigen__2 @ eigen__4 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: $i] :
        ( ( in @ X1 @ ( powerset @ eigen__0 ) )
       => ( ( subset @ eigen__2 @ X1 )
         => ( subset @ ( binintersect @ eigen__1 @ eigen__2 ) @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( in @ eigen__2 @ ( powerset @ eigen__0 ) )
     => ! [X1: $i] :
          ( ( in @ X1 @ ( powerset @ eigen__0 ) )
         => ( ( subset @ eigen__1 @ X1 )
           => ( subset @ ( binintersect @ eigen__1 @ eigen__2 ) @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( in @ eigen__1 @ ( powerset @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ( in @ ( binintersect @ eigen__1 @ eigen__2 ) @ ( powerset @ eigen__0 ) )
     => ! [X1: $i] :
          ( ( in @ X1 @ ( powerset @ eigen__0 ) )
         => ! [X2: $i] :
              ( ( in @ X2 @ ( powerset @ eigen__0 ) )
             => ( ( subset @ ( binintersect @ eigen__1 @ eigen__2 ) @ X1 )
               => ( ( subset @ ( binintersect @ eigen__1 @ eigen__2 ) @ X2 )
                 => ( subset @ ( binintersect @ eigen__1 @ eigen__2 ) @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: $i,X2: $i] :
        ( ( in @ X2 @ ( powerset @ X1 ) )
       => ! [X3: $i] :
            ( ( in @ X3 @ ( powerset @ X1 ) )
           => ! [X4: $i] :
                ( ( in @ X4 @ ( powerset @ X1 ) )
               => ( ( subset @ X2 @ X4 )
                 => ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: $i] :
        ( ( in @ X1 @ ( powerset @ eigen__0 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ ( powerset @ eigen__0 ) )
           => ( ( subset @ eigen__1 @ X2 )
             => ( subset @ ( binintersect @ eigen__1 @ X1 ) @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( in @ eigen__3 @ ( powerset @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ! [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,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( in @ ( binintersect @ eigen__1 @ eigen__2 ) @ ( powerset @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( ( subset @ ( binintersect @ eigen__1 @ eigen__2 ) @ eigen__3 )
     => ( sP1
       => ( subset @ ( binintersect @ eigen__1 @ eigen__2 ) @ ( binintersect @ eigen__3 @ eigen__4 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( sP5
     => ! [X1: $i] :
          ( ( in @ X1 @ ( powerset @ eigen__0 ) )
         => ! [X2: $i] :
              ( ( in @ X2 @ ( powerset @ eigen__0 ) )
             => ( ( subset @ X1 @ X2 )
               => ( subset @ ( binintersect @ eigen__1 @ X1 ) @ X2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( sP9
     => ( ( subset @ eigen__1 @ eigen__3 )
       => ( subset @ ( binintersect @ eigen__1 @ eigen__2 ) @ eigen__3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( in @ eigen__2 @ ( powerset @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ! [X1: $i] :
        ( ( in @ X1 @ ( powerset @ eigen__0 ) )
       => ( ( subset @ ( binintersect @ eigen__1 @ eigen__2 ) @ eigen__3 )
         => ( ( subset @ ( binintersect @ eigen__1 @ eigen__2 ) @ X1 )
           => ( subset @ ( binintersect @ eigen__1 @ eigen__2 ) @ ( binintersect @ eigen__3 @ X1 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

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

thf(sP18,plain,
    ( sP18
  <=> ( sP9
     => sP16 ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ! [X1: $i] :
        ( ( in @ X1 @ ( powerset @ eigen__0 ) )
       => ( ( subset @ eigen__1 @ X1 )
         => ( subset @ ( binintersect @ eigen__1 @ eigen__2 ) @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ( subset @ ( binintersect @ eigen__1 @ eigen__2 ) @ eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ( ( in @ eigen__4 @ ( powerset @ eigen__0 ) )
     => sP12 ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ! [X1: $i] :
        ( ( in @ X1 @ ( powerset @ eigen__0 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ ( powerset @ eigen__0 ) )
           => ! [X3: $i] :
                ( ( in @ X3 @ ( powerset @ eigen__0 ) )
               => ( ( subset @ X1 @ X3 )
                 => ( subset @ ( binintersect @ X1 @ X2 ) @ X3 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ( sP2
     => sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> ! [X1: $i,X2: $i] :
        ( ( in @ X2 @ ( powerset @ X1 ) )
       => ! [X3: $i] :
            ( ( in @ X3 @ ( powerset @ X1 ) )
           => ! [X4: $i] :
                ( ( in @ X4 @ ( powerset @ X1 ) )
               => ( ( subset @ X3 @ X4 )
                 => ( subset @ ( binintersect @ X2 @ X3 ) @ X4 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ! [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,[sP25])]) ).

thf(sP26,plain,
    ( sP26
  <=> ! [X1: $i] :
        ( ( in @ X1 @ ( powerset @ eigen__0 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ ( powerset @ eigen__0 ) )
           => ( ( subset @ ( binintersect @ eigen__1 @ eigen__2 ) @ X1 )
             => ( ( subset @ ( binintersect @ eigen__1 @ eigen__2 ) @ X2 )
               => ( subset @ ( binintersect @ eigen__1 @ eigen__2 ) @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
    ( sP27
  <=> ( ( subset @ eigen__1 @ eigen__3 )
     => sP20 ) ),
    introduced(definition,[new_symbols(definition,[sP27])]) ).

thf(sP28,plain,
    ( sP28
  <=> ( sP15
     => sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP28])]) ).

thf(sP29,plain,
    ( sP29
  <=> ( subset @ eigen__1 @ eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP29])]) ).

thf(sP30,plain,
    ( sP30
  <=> ( subset @ ( binintersect @ eigen__1 @ eigen__2 ) @ ( binintersect @ eigen__3 @ eigen__4 ) ) ),
    introduced(definition,[new_symbols(definition,[sP30])]) ).

thf(sP31,plain,
    ( sP31
  <=> ! [X1: $i] :
        ( ( in @ X1 @ ( powerset @ eigen__0 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ ( powerset @ eigen__0 ) )
           => ! [X3: $i] :
                ( ( in @ X3 @ ( powerset @ eigen__0 ) )
               => ( ( subset @ X2 @ X3 )
                 => ( subset @ ( binintersect @ X1 @ X2 ) @ X3 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP31])]) ).

thf(sP32,plain,
    ( sP32
  <=> ! [X1: $i,X2: $i] :
        ( ( in @ X2 @ ( powerset @ X1 ) )
       => ! [X3: $i] :
            ( ( in @ X3 @ ( powerset @ X1 ) )
           => ! [X4: $i] :
                ( ( in @ X4 @ ( powerset @ X1 ) )
               => ( ( subset @ X2 @ X3 )
                 => ( ( subset @ X2 @ X4 )
                   => ( subset @ X2 @ ( binintersect @ X3 @ X4 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP32])]) ).

thf(sP33,plain,
    ( sP33
  <=> ( sP5
     => sP17 ) ),
    introduced(definition,[new_symbols(definition,[sP33])]) ).

thf(sP34,plain,
    ( sP34
  <=> ( sP15
     => sP11 ) ),
    introduced(definition,[new_symbols(definition,[sP34])]) ).

thf(sP35,plain,
    ( sP35
  <=> ! [X1: $i] :
        ( ( in @ X1 @ ( powerset @ eigen__0 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ ( powerset @ eigen__0 ) )
           => ! [X3: $i] :
                ( ( in @ X3 @ ( powerset @ eigen__0 ) )
               => ( ( subset @ X1 @ X2 )
                 => ( ( subset @ X1 @ X3 )
                   => ( subset @ X1 @ ( binintersect @ X2 @ X3 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP35])]) ).

thf(sP36,plain,
    ( sP36
  <=> ! [X1: $i] :
        ( ( in @ X1 @ ( powerset @ eigen__0 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ ( powerset @ eigen__0 ) )
           => ( ( subset @ X1 @ X2 )
             => ( subset @ ( binintersect @ eigen__1 @ X1 ) @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP36])]) ).

thf(sP37,plain,
    ( sP37
  <=> ( in @ eigen__4 @ ( powerset @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP37])]) ).

thf(sP38,plain,
    ( sP38
  <=> ( sP5
     => sP8 ) ),
    introduced(definition,[new_symbols(definition,[sP38])]) ).

thf(sP39,plain,
    ( sP39
  <=> ( sP1
     => sP30 ) ),
    introduced(definition,[new_symbols(definition,[sP39])]) ).

thf(sP40,plain,
    ( sP40
  <=> ( sP37
     => sP23 ) ),
    introduced(definition,[new_symbols(definition,[sP40])]) ).

thf(def_binintersectT_lem,definition,
    binintersectT_lem = sP25 ).

thf(def_woz13rule1,definition,
    woz13rule1 = sP7 ).

thf(def_woz13rule2,definition,
    woz13rule2 = sP24 ).

thf(def_woz13rule3,definition,
    woz13rule3 = sP32 ).

thf(woz13rule4,conjecture,
    ( sP25
   => ( sP7
     => ( sP24
       => ( sP32
         => ! [X1: $i,X2: $i] :
              ( ( in @ X2 @ ( powerset @ X1 ) )
             => ! [X3: $i] :
                  ( ( in @ X3 @ ( powerset @ X1 ) )
                 => ! [X4: $i] :
                      ( ( in @ X4 @ ( powerset @ X1 ) )
                     => ! [X5: $i] :
                          ( ( in @ X5 @ ( powerset @ X1 ) )
                         => ( ( subset @ X2 @ X4 )
                           => ( ( subset @ X3 @ X5 )
                             => ( subset @ ( binintersect @ X2 @ X3 ) @ ( binintersect @ X4 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ( sP25
     => ( sP7
       => ( sP24
         => ( sP32
           => ! [X1: $i,X2: $i] :
                ( ( in @ X2 @ ( powerset @ X1 ) )
               => ! [X3: $i] :
                    ( ( in @ X3 @ ( powerset @ X1 ) )
                   => ! [X4: $i] :
                        ( ( in @ X4 @ ( powerset @ X1 ) )
                       => ! [X5: $i] :
                            ( ( in @ X5 @ ( powerset @ X1 ) )
                           => ( ( subset @ X2 @ X4 )
                             => ( ( subset @ X3 @ X5 )
                               => ( subset @ ( binintersect @ X2 @ X3 ) @ ( binintersect @ X4 @ X5 ) ) ) ) ) ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[woz13rule4]) ).

thf(h1,assumption,
    sP25,
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ( sP7
     => ( sP24
       => ( sP32
         => ! [X1: $i,X2: $i] :
              ( ( in @ X2 @ ( powerset @ X1 ) )
             => ! [X3: $i] :
                  ( ( in @ X3 @ ( powerset @ X1 ) )
                 => ! [X4: $i] :
                      ( ( in @ X4 @ ( powerset @ X1 ) )
                     => ! [X5: $i] :
                          ( ( in @ X5 @ ( powerset @ X1 ) )
                         => ( ( subset @ X2 @ X4 )
                           => ( ( subset @ X3 @ X5 )
                             => ( subset @ ( binintersect @ X2 @ X3 ) @ ( binintersect @ X4 @ X5 ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

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

thf(h4,assumption,
    ~ ( sP24
     => ( sP32
       => ! [X1: $i,X2: $i] :
            ( ( in @ X2 @ ( powerset @ X1 ) )
           => ! [X3: $i] :
                ( ( in @ X3 @ ( powerset @ X1 ) )
               => ! [X4: $i] :
                    ( ( in @ X4 @ ( powerset @ X1 ) )
                   => ! [X5: $i] :
                        ( ( in @ X5 @ ( powerset @ X1 ) )
                       => ( ( subset @ X2 @ X4 )
                         => ( ( subset @ X3 @ X5 )
                           => ( subset @ ( binintersect @ X2 @ X3 ) @ ( binintersect @ X4 @ X5 ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    sP24,
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ ( sP32
     => ! [X1: $i,X2: $i] :
          ( ( in @ X2 @ ( powerset @ X1 ) )
         => ! [X3: $i] :
              ( ( in @ X3 @ ( powerset @ X1 ) )
             => ! [X4: $i] :
                  ( ( in @ X4 @ ( powerset @ X1 ) )
                 => ! [X5: $i] :
                      ( ( in @ X5 @ ( powerset @ X1 ) )
                     => ( ( subset @ X2 @ X4 )
                       => ( ( subset @ X3 @ X5 )
                         => ( subset @ ( binintersect @ X2 @ X3 ) @ ( binintersect @ X4 @ X5 ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    sP32,
    introduced(assumption,[]) ).

thf(h8,assumption,
    ~ ! [X1: $i,X2: $i] :
        ( ( in @ X2 @ ( powerset @ X1 ) )
       => ! [X3: $i] :
            ( ( in @ X3 @ ( powerset @ X1 ) )
           => ! [X4: $i] :
                ( ( in @ X4 @ ( powerset @ X1 ) )
               => ! [X5: $i] :
                    ( ( in @ X5 @ ( powerset @ X1 ) )
                   => ( ( subset @ X2 @ X4 )
                     => ( ( subset @ X3 @ X5 )
                       => ( subset @ ( binintersect @ X2 @ X3 ) @ ( binintersect @ X4 @ X5 ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ ! [X1: $i] :
        ( ( in @ X1 @ ( powerset @ eigen__0 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ ( powerset @ eigen__0 ) )
           => ! [X3: $i] :
                ( ( in @ X3 @ ( powerset @ eigen__0 ) )
               => ! [X4: $i] :
                    ( ( in @ X4 @ ( powerset @ eigen__0 ) )
                   => ( ( subset @ X1 @ X3 )
                     => ( ( subset @ X2 @ X4 )
                       => ( subset @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X3 @ X4 ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h10,assumption,
    ~ ( sP5
     => ! [X1: $i] :
          ( ( in @ X1 @ ( powerset @ eigen__0 ) )
         => ! [X2: $i] :
              ( ( in @ X2 @ ( powerset @ eigen__0 ) )
             => ! [X3: $i] :
                  ( ( in @ X3 @ ( powerset @ eigen__0 ) )
                 => ( ( subset @ eigen__1 @ X2 )
                   => ( ( subset @ X1 @ X3 )
                     => ( subset @ ( binintersect @ eigen__1 @ X1 ) @ ( binintersect @ X2 @ X3 ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h11,assumption,
    sP5,
    introduced(assumption,[]) ).

thf(h12,assumption,
    ~ ! [X1: $i] :
        ( ( in @ X1 @ ( powerset @ eigen__0 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ ( powerset @ eigen__0 ) )
           => ! [X3: $i] :
                ( ( in @ X3 @ ( powerset @ eigen__0 ) )
               => ( ( subset @ eigen__1 @ X2 )
                 => ( ( subset @ X1 @ X3 )
                   => ( subset @ ( binintersect @ eigen__1 @ X1 ) @ ( binintersect @ X2 @ X3 ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h13,assumption,
    ~ ( sP15
     => ! [X1: $i] :
          ( ( in @ X1 @ ( powerset @ eigen__0 ) )
         => ! [X2: $i] :
              ( ( in @ X2 @ ( powerset @ eigen__0 ) )
             => ( ( subset @ eigen__1 @ X1 )
               => ( ( subset @ eigen__2 @ X2 )
                 => ( subset @ ( binintersect @ eigen__1 @ eigen__2 ) @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h14,assumption,
    sP15,
    introduced(assumption,[]) ).

thf(h15,assumption,
    ~ ! [X1: $i] :
        ( ( in @ X1 @ ( powerset @ eigen__0 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ ( powerset @ eigen__0 ) )
           => ( ( subset @ eigen__1 @ X1 )
             => ( ( subset @ eigen__2 @ X2 )
               => ( subset @ ( binintersect @ eigen__1 @ eigen__2 ) @ ( binintersect @ X1 @ X2 ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h16,assumption,
    ~ ( sP9
     => ! [X1: $i] :
          ( ( in @ X1 @ ( powerset @ eigen__0 ) )
         => ( sP29
           => ( ( subset @ eigen__2 @ X1 )
             => ( subset @ ( binintersect @ eigen__1 @ eigen__2 ) @ ( binintersect @ eigen__3 @ X1 ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h17,assumption,
    sP9,
    introduced(assumption,[]) ).

thf(h18,assumption,
    ~ ! [X1: $i] :
        ( ( in @ X1 @ ( powerset @ eigen__0 ) )
       => ( sP29
         => ( ( subset @ eigen__2 @ X1 )
           => ( subset @ ( binintersect @ eigen__1 @ eigen__2 ) @ ( binintersect @ eigen__3 @ X1 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h19,assumption,
    ~ ( sP37
     => ( sP29
       => ( sP2
         => sP30 ) ) ),
    introduced(assumption,[]) ).

thf(h20,assumption,
    sP37,
    introduced(assumption,[]) ).

thf(h21,assumption,
    ~ ( sP29
     => ( sP2
       => sP30 ) ),
    introduced(assumption,[]) ).

thf(h22,assumption,
    sP29,
    introduced(assumption,[]) ).

thf(h23,assumption,
    ~ ( sP2
     => sP30 ),
    introduced(assumption,[]) ).

thf(h24,assumption,
    sP2,
    introduced(assumption,[]) ).

thf(h25,assumption,
    ~ sP30,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP17
    | sP34 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP34
    | ~ sP15
    | sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP25
    | sP10 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP10
    | sP33 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP33
    | ~ sP5
    | sP17 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP19
    | sP14 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP14
    | ~ sP9
    | sP27 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP27
    | ~ sP29
    | sP20 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP8
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP4
    | ~ sP15
    | sP19 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP7
    | sP22 ),
    inference(all_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP22
    | sP38 ),
    inference(all_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP38
    | ~ sP5
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP3
    | sP40 ),
    inference(all_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP40
    | ~ sP37
    | sP23 ),
    inference(prop_rule,[status(thm)],]) ).

thf(16,plain,
    ( ~ sP23
    | ~ sP2
    | sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(17,plain,
    ( ~ sP36
    | sP28 ),
    inference(all_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP28
    | ~ sP15
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(19,plain,
    ( ~ sP24
    | sP31 ),
    inference(all_rule,[status(thm)],]) ).

thf(20,plain,
    ( ~ sP31
    | sP13 ),
    inference(all_rule,[status(thm)],]) ).

thf(21,plain,
    ( ~ sP13
    | ~ sP5
    | sP36 ),
    inference(prop_rule,[status(thm)],]) ).

thf(22,plain,
    ( ~ sP35
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(23,plain,
    ( ~ sP6
    | ~ sP11
    | sP26 ),
    inference(prop_rule,[status(thm)],]) ).

thf(24,plain,
    ( ~ sP26
    | sP18 ),
    inference(all_rule,[status(thm)],]) ).

thf(25,plain,
    ( ~ sP18
    | ~ sP9
    | sP16 ),
    inference(prop_rule,[status(thm)],]) ).

thf(26,plain,
    ( ~ sP16
    | sP21 ),
    inference(all_rule,[status(thm)],]) ).

thf(27,plain,
    ( ~ sP21
    | ~ sP37
    | sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(28,plain,
    ( ~ sP12
    | ~ sP20
    | sP39 ),
    inference(prop_rule,[status(thm)],]) ).

thf(29,plain,
    ( ~ sP39
    | ~ sP1
    | sP30 ),
    inference(prop_rule,[status(thm)],]) ).

thf(30,plain,
    ( ~ sP32
    | sP35 ),
    inference(all_rule,[status(thm)],]) ).

thf(31,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h24,h25,h22,h23,h20,h21,h19,h17,h18,h16,h14,h15,h13,h11,h12,h10,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,h1,h3,h5,h7,h11,h14,h17,h20,h22,h24,h25]) ).

thf(32,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h22,h23,h20,h21,h19,h17,h18,h16,h14,h15,h13,h11,h12,h10,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h24,h25])],[h23,31,h24,h25]) ).

thf(33,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h20,h21,h19,h17,h18,h16,h14,h15,h13,h11,h12,h10,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h22,h23])],[h21,32,h22,h23]) ).

thf(34,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h19,h17,h18,h16,h14,h15,h13,h11,h12,h10,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h20,h21])],[h19,33,h20,h21]) ).

thf(35,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h17,h18,h16,h14,h15,h13,h11,h12,h10,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h19]),tab_negall(eigenvar,eigen__4)],[h18,34,h19]) ).

thf(36,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h16,h14,h15,h13,h11,h12,h10,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h17,h18])],[h16,35,h17,h18]) ).

thf(37,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h14,h15,h13,h11,h12,h10,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__3)],[h15,36,h16]) ).

thf(38,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])],[h13,37,h14,h15]) ).

thf(39,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)],[h12,38,h13]) ).

thf(40,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h10,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h10,39,h11,h12]) ).

thf(41,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)],[h9,40,h10]) ).

thf(42,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)],[h8,41,h9]) ).

thf(43,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,42,h7,h8]) ).

thf(44,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,43,h5,h6]) ).

thf(45,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,44,h3,h4]) ).

thf(46,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,45,h1,h2]) ).

thf(0,theorem,
    ( sP25
   => ( sP7
     => ( sP24
       => ( sP32
         => ! [X1: $i,X2: $i] :
              ( ( in @ X2 @ ( powerset @ X1 ) )
             => ! [X3: $i] :
                  ( ( in @ X3 @ ( powerset @ X1 ) )
                 => ! [X4: $i] :
                      ( ( in @ X4 @ ( powerset @ X1 ) )
                     => ! [X5: $i] :
                          ( ( in @ X5 @ ( powerset @ X1 ) )
                         => ( ( subset @ X2 @ X4 )
                           => ( ( subset @ X3 @ X5 )
                             => ( subset @ ( binintersect @ X2 @ X3 ) @ ( binintersect @ X4 @ X5 ) ) ) ) ) ) ) ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[46,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SEU762^2 : TPTP v8.1.0. Released v3.7.0.
% 0.03/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35  % Computer : n020.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  : 600
% 0.13/0.35  % DateTime : Sun Jun 19 05:58:48 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.37/0.55  % SZS status Theorem
% 0.37/0.55  % Mode: mode213
% 0.37/0.55  % Inferences: 11
% 0.37/0.55  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------