TSTP Solution File: SEU742^2 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEU742^2 : 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 : n003.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Tue Jul 19 14:00:21 EDT 2022

% Result   : Theorem 0.19s 0.59s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

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

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

thf(sP2,plain,
    ( sP2
  <=> ( ( in @ eigen__2 @ ( powerset @ eigen__0 ) )
     => ! [X1: $i] :
          ( ( in @ X1 @ ( powerset @ eigen__0 ) )
         => ! [X2: $i] :
              ( ( in @ X2 @ eigen__0 )
             => ( ( in @ X2 @ ( binintersect @ eigen__1 @ eigen__2 ) )
               => ( in @ X2 @ ( binunion @ eigen__1 @ X1 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: $i,X2: $i] :
        ( ( in @ X2 @ ( powerset @ X1 ) )
       => ! [X3: $i] :
            ( ( in @ X3 @ ( powerset @ X1 ) )
           => ! [X4: $i] :
                ( ( in @ X4 @ ( powerset @ X1 ) )
               => ! [X5: $i] :
                    ( ( in @ X5 @ X1 )
                   => ( ( in @ X5 @ ( binintersect @ X2 @ X3 ) )
                     => ( in @ X5 @ ( binunion @ X3 @ X4 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( sP1
     => ( in @ eigen__4 @ ( binunion @ eigen__2 @ eigen__3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: $i] :
        ( ( in @ X1 @ ( powerset @ eigen__0 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ ( powerset @ eigen__0 ) )
           => ! [X3: $i] :
                ( ( in @ X3 @ eigen__0 )
               => ( ( in @ X3 @ ( binintersect @ eigen__1 @ X1 ) )
                 => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ( in @ eigen__4 @ ( binunion @ eigen__1 @ eigen__3 ) )
     => ( ( in @ eigen__4 @ ( binunion @ eigen__2 @ eigen__3 ) )
       => ( in @ eigen__4 @ ( binintersect @ ( binunion @ eigen__1 @ eigen__3 ) @ ( binunion @ eigen__2 @ eigen__3 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( in @ eigen__1 @ ( powerset @ eigen__0 ) )
     => ! [X1: $i] :
          ( ( in @ X1 @ ( powerset @ eigen__0 ) )
         => ! [X2: $i] :
              ( ( in @ X2 @ ( powerset @ eigen__0 ) )
             => ! [X3: $i] :
                  ( ( in @ X3 @ eigen__0 )
                 => ( ( in @ X3 @ ( binintersect @ eigen__1 @ X1 ) )
                   => ( in @ X3 @ ( binunion @ eigen__1 @ X2 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: $i] :
        ( ( in @ X1 @ ( powerset @ eigen__0 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ ( powerset @ eigen__0 ) )
           => ! [X3: $i] :
                ( ( in @ X3 @ eigen__0 )
               => ( ( in @ X3 @ ( binintersect @ eigen__1 @ X1 ) )
                 => ( in @ X3 @ ( binunion @ eigen__1 @ X2 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( in @ eigen__2 @ ( powerset @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( ( in @ eigen__4 @ ( binunion @ eigen__2 @ eigen__3 ) )
     => ( in @ eigen__4 @ ( binintersect @ ( binunion @ eigen__1 @ eigen__3 ) @ ( binunion @ eigen__2 @ eigen__3 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( ( in @ eigen__4 @ eigen__0 )
     => ( sP1
       => ( in @ eigen__4 @ ( binunion @ eigen__1 @ eigen__3 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ! [X1: $i] :
        ( ( in @ X1 @ ( powerset @ eigen__0 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ eigen__0 )
           => ( ( in @ X2 @ ( binintersect @ eigen__1 @ eigen__2 ) )
             => ( in @ X2 @ ( binunion @ eigen__1 @ X1 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( ( in @ eigen__4 @ eigen__0 )
     => sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( in @ eigen__1 @ ( powerset @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ! [X1: $i] :
        ( ( in @ X1 @ eigen__0 )
       => ( ( in @ X1 @ ( binintersect @ eigen__1 @ eigen__2 ) )
         => ( in @ X1 @ ( binunion @ eigen__2 @ eigen__3 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( in @ eigen__4 @ ( binunion @ eigen__2 @ eigen__3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ! [X1: $i,X2: $i,X3: $i] :
        ( ( in @ X3 @ X1 )
       => ( ( in @ X3 @ X2 )
         => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ( sP14
     => sP5 ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ( ( in @ eigen__3 @ ( powerset @ eigen__0 ) )
     => sP15 ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ( sP9
     => ! [X1: $i] :
          ( ( in @ X1 @ ( powerset @ eigen__0 ) )
         => ! [X2: $i] :
              ( ( in @ X2 @ eigen__0 )
             => ( ( in @ X2 @ ( binintersect @ eigen__1 @ eigen__2 ) )
               => ( in @ X2 @ ( binunion @ eigen__2 @ X1 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

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

thf(sP22,plain,
    ( sP22
  <=> ! [X1: $i] :
        ( ( in @ X1 @ ( powerset @ eigen__0 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ eigen__0 )
           => ( ( in @ X2 @ ( binintersect @ eigen__1 @ eigen__2 ) )
             => ( in @ X2 @ ( binunion @ eigen__2 @ X1 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ! [X1: $i,X2: $i] :
        ( ( in @ X2 @ ( binunion @ eigen__1 @ eigen__3 ) )
       => ( ( in @ X2 @ X1 )
         => ( in @ X2 @ ( binintersect @ ( binunion @ eigen__1 @ eigen__3 ) @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> ( in @ eigen__4 @ ( binintersect @ ( binunion @ eigen__1 @ eigen__3 ) @ ( binunion @ eigen__2 @ eigen__3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ! [X1: $i] :
        ( ( in @ X1 @ eigen__0 )
       => ( ( in @ X1 @ ( binintersect @ eigen__1 @ eigen__2 ) )
         => ( in @ X1 @ ( binunion @ eigen__1 @ eigen__3 ) ) ) ) ),
    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 @ ( powerset @ X1 ) )
               => ! [X5: $i] :
                    ( ( in @ X5 @ X1 )
                   => ( ( in @ X5 @ ( binintersect @ X2 @ X3 ) )
                     => ( in @ X5 @ ( binunion @ X2 @ X4 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
    ( sP27
  <=> ( ( in @ eigen__3 @ ( powerset @ eigen__0 ) )
     => sP25 ) ),
    introduced(definition,[new_symbols(definition,[sP27])]) ).

thf(sP28,plain,
    ( sP28
  <=> ! [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 @ eigen__0 )
                   => ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
                     => ( in @ X4 @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP28])]) ).

thf(sP29,plain,
    ( sP29
  <=> ( in @ eigen__4 @ ( binunion @ eigen__1 @ eigen__3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP29])]) ).

thf(sP30,plain,
    ( sP30
  <=> ! [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 @ eigen__0 )
                   => ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
                     => ( in @ X4 @ ( binunion @ X1 @ X3 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP30])]) ).

thf(sP31,plain,
    ( sP31
  <=> ! [X1: $i] :
        ( ( in @ X1 @ ( binunion @ eigen__1 @ eigen__3 ) )
       => ( ( in @ X1 @ ( binunion @ eigen__2 @ eigen__3 ) )
         => ( in @ X1 @ ( binintersect @ ( binunion @ eigen__1 @ eigen__3 ) @ ( binunion @ eigen__2 @ eigen__3 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP31])]) ).

thf(sP32,plain,
    ( sP32
  <=> ( in @ eigen__3 @ ( powerset @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP32])]) ).

thf(sP33,plain,
    ( sP33
  <=> ( sP1
     => sP29 ) ),
    introduced(definition,[new_symbols(definition,[sP33])]) ).

thf(def_binintersectI,definition,
    binintersectI = sP17 ).

thf(def_inIntersectImpInUnion,definition,
    inIntersectImpInUnion = sP26 ).

thf(def_inIntersectImpInUnion2,definition,
    inIntersectImpInUnion2 = sP3 ).

thf(inIntersectImpInIntersectUnions,conjecture,
    ( sP17
   => ( sP26
     => ( sP3
       => ! [X1: $i,X2: $i] :
            ( ( in @ X2 @ ( powerset @ X1 ) )
           => ! [X3: $i] :
                ( ( in @ X3 @ ( powerset @ X1 ) )
               => ! [X4: $i] :
                    ( ( in @ X4 @ ( powerset @ X1 ) )
                   => ! [X5: $i] :
                        ( ( in @ X5 @ X1 )
                       => ( ( in @ X5 @ ( binintersect @ X2 @ X3 ) )
                         => ( in @ X5 @ ( binintersect @ ( binunion @ X2 @ X4 ) @ ( binunion @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ( sP17
     => ( sP26
       => ( sP3
         => ! [X1: $i,X2: $i] :
              ( ( in @ X2 @ ( powerset @ X1 ) )
             => ! [X3: $i] :
                  ( ( in @ X3 @ ( powerset @ X1 ) )
                 => ! [X4: $i] :
                      ( ( in @ X4 @ ( powerset @ X1 ) )
                     => ! [X5: $i] :
                          ( ( in @ X5 @ X1 )
                         => ( ( in @ X5 @ ( binintersect @ X2 @ X3 ) )
                           => ( in @ X5 @ ( binintersect @ ( binunion @ X2 @ X4 ) @ ( binunion @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[inIntersectImpInIntersectUnions]) ).

thf(h1,assumption,
    sP17,
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ( sP26
     => ( sP3
       => ! [X1: $i,X2: $i] :
            ( ( in @ X2 @ ( powerset @ X1 ) )
           => ! [X3: $i] :
                ( ( in @ X3 @ ( powerset @ X1 ) )
               => ! [X4: $i] :
                    ( ( in @ X4 @ ( powerset @ X1 ) )
                   => ! [X5: $i] :
                        ( ( in @ X5 @ X1 )
                       => ( ( in @ X5 @ ( binintersect @ X2 @ X3 ) )
                         => ( in @ X5 @ ( binintersect @ ( binunion @ X2 @ X4 ) @ ( binunion @ X3 @ X4 ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    sP26,
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ( sP3
     => ! [X1: $i,X2: $i] :
          ( ( in @ X2 @ ( powerset @ X1 ) )
         => ! [X3: $i] :
              ( ( in @ X3 @ ( powerset @ X1 ) )
             => ! [X4: $i] :
                  ( ( in @ X4 @ ( powerset @ X1 ) )
                 => ! [X5: $i] :
                      ( ( in @ X5 @ X1 )
                     => ( ( in @ X5 @ ( binintersect @ X2 @ X3 ) )
                       => ( in @ X5 @ ( binintersect @ ( binunion @ X2 @ X4 ) @ ( binunion @ X3 @ X4 ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    sP3,
    introduced(assumption,[]) ).

thf(h6,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 @ X1 )
                   => ( ( in @ X5 @ ( binintersect @ X2 @ X3 ) )
                     => ( in @ X5 @ ( binintersect @ ( binunion @ X2 @ X4 ) @ ( binunion @ X3 @ X4 ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h7,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 @ eigen__0 )
                   => ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
                     => ( in @ X4 @ ( binintersect @ ( binunion @ X1 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h8,assumption,
    ~ ( sP14
     => ! [X1: $i] :
          ( ( in @ X1 @ ( powerset @ eigen__0 ) )
         => ! [X2: $i] :
              ( ( in @ X2 @ ( powerset @ eigen__0 ) )
             => ! [X3: $i] :
                  ( ( in @ X3 @ eigen__0 )
                 => ( ( in @ X3 @ ( binintersect @ eigen__1 @ X1 ) )
                   => ( in @ X3 @ ( binintersect @ ( binunion @ eigen__1 @ X2 ) @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h9,assumption,
    sP14,
    introduced(assumption,[]) ).

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

thf(h11,assumption,
    ~ ( sP9
     => ! [X1: $i] :
          ( ( in @ X1 @ ( powerset @ eigen__0 ) )
         => ! [X2: $i] :
              ( ( in @ X2 @ eigen__0 )
             => ( ( in @ X2 @ ( binintersect @ eigen__1 @ eigen__2 ) )
               => ( in @ X2 @ ( binintersect @ ( binunion @ eigen__1 @ X1 ) @ ( binunion @ eigen__2 @ X1 ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h12,assumption,
    sP9,
    introduced(assumption,[]) ).

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

thf(h14,assumption,
    ~ ( sP32
     => ! [X1: $i] :
          ( ( in @ X1 @ eigen__0 )
         => ( ( in @ X1 @ ( binintersect @ eigen__1 @ eigen__2 ) )
           => ( in @ X1 @ ( binintersect @ ( binunion @ eigen__1 @ eigen__3 ) @ ( binunion @ eigen__2 @ eigen__3 ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h15,assumption,
    sP32,
    introduced(assumption,[]) ).

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

thf(h17,assumption,
    ~ ( sP21
     => ( sP1
       => sP24 ) ),
    introduced(assumption,[]) ).

thf(h18,assumption,
    sP21,
    introduced(assumption,[]) ).

thf(h19,assumption,
    ~ ( sP1
     => sP24 ),
    introduced(assumption,[]) ).

thf(h20,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h21,assumption,
    ~ sP24,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP17
    | sP23 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP23
    | sP31 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP31
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP6
    | ~ sP29
    | sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP10
    | ~ sP16
    | sP24 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP25
    | sP11 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP11
    | ~ sP21
    | sP33 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP33
    | ~ sP1
    | sP29 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP12
    | sP27 ),
    inference(all_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP27
    | ~ sP32
    | sP25 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP8
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP2
    | ~ sP9
    | sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP26
    | sP30 ),
    inference(all_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP30
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP7
    | ~ sP14
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(16,plain,
    ( ~ sP15
    | sP13 ),
    inference(all_rule,[status(thm)],]) ).

thf(17,plain,
    ( ~ sP13
    | ~ sP21
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP4
    | ~ sP1
    | sP16 ),
    inference(prop_rule,[status(thm)],]) ).

thf(19,plain,
    ( ~ sP22
    | sP19 ),
    inference(all_rule,[status(thm)],]) ).

thf(20,plain,
    ( ~ sP19
    | ~ sP32
    | sP15 ),
    inference(prop_rule,[status(thm)],]) ).

thf(21,plain,
    ( ~ sP5
    | sP20 ),
    inference(all_rule,[status(thm)],]) ).

thf(22,plain,
    ( ~ sP20
    | ~ sP9
    | sP22 ),
    inference(prop_rule,[status(thm)],]) ).

thf(23,plain,
    ( ~ sP3
    | sP28 ),
    inference(all_rule,[status(thm)],]) ).

thf(24,plain,
    ( ~ sP28
    | sP18 ),
    inference(all_rule,[status(thm)],]) ).

thf(25,plain,
    ( ~ sP18
    | ~ sP14
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(26,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h20,h21,h18,h19,h17,h15,h16,h14,h12,h13,h11,h9,h10,h8,h7,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,h1,h3,h5,h9,h12,h15,h18,h20,h21]) ).

thf(27,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h18,h19,h17,h15,h16,h14,h12,h13,h11,h9,h10,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h20,h21])],[h19,26,h20,h21]) ).

thf(28,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h17,h15,h16,h14,h12,h13,h11,h9,h10,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h18,h19])],[h17,27,h18,h19]) ).

thf(29,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h15,h16,h14,h12,h13,h11,h9,h10,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__4)],[h16,28,h17]) ).

thf(30,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h14,h12,h13,h11,h9,h10,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h15,h16])],[h14,29,h15,h16]) ).

thf(31,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h12,h13,h11,h9,h10,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__3)],[h13,30,h14]) ).

thf(32,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h11,h9,h10,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h12,h13])],[h11,31,h12,h13]) ).

thf(33,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h9,h10,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__2)],[h10,32,h11]) ).

thf(34,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h8,33,h9,h10]) ).

thf(35,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__1)],[h7,34,h8]) ).

thf(36,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__0)],[h6,35,h7]) ).

thf(37,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,36,h5,h6]) ).

thf(38,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,37,h3,h4]) ).

thf(39,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,38,h1,h2]) ).

thf(0,theorem,
    ( sP17
   => ( sP26
     => ( sP3
       => ! [X1: $i,X2: $i] :
            ( ( in @ X2 @ ( powerset @ X1 ) )
           => ! [X3: $i] :
                ( ( in @ X3 @ ( powerset @ X1 ) )
               => ! [X4: $i] :
                    ( ( in @ X4 @ ( powerset @ X1 ) )
                   => ! [X5: $i] :
                        ( ( in @ X5 @ X1 )
                       => ( ( in @ X5 @ ( binintersect @ X2 @ X3 ) )
                         => ( in @ X5 @ ( binintersect @ ( binunion @ X2 @ X4 ) @ ( binunion @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[39,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU742^2 : TPTP v8.1.0. Released v3.7.0.
% 0.11/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n003.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jun 20 09:53:59 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.59  % SZS status Theorem
% 0.19/0.59  % Mode: mode213
% 0.19/0.59  % Inferences: 9
% 0.19/0.59  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------