TSTP Solution File: SEU707^2 by Lash---1.13

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEU707^2 : 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 : n009.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 17:22:42 EDT 2023

% Result   : Theorem 0.20s 0.73s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   92
% Syntax   : Number of formulae    :  107 (  26 unt;   9 typ;   5 def)
%            Number of atoms       :  352 (  96 equ;   3 cnn)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  621 ( 161   ~;  45   |;   6   &; 219   @)
%                                         (  32 <=>; 158  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   49 (  46 usr;  44 con; 0-2 aty)
%            Number of variables   :  121 (  53   ^;  68   !;   0   ?; 121   :)

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

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

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

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

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

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

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

thf(ty_eigen__5,type,
    eigen__5: $i ).

thf(ty_singleton,type,
    singleton: $i > $o ).

thf(h0,assumption,
    ! [X1: $i > $o,X2: $i] :
      ( ( X1 @ X2 )
     => ( X1 @ ( eps__0 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(eigendef_eigen__5,definition,
    ( eigen__5
    = ( eps__0
      @ ^ [X1: $i] :
          ( ( X1 = eigen__2 )
         != ( ( eigen__1
             => ( X1 != eigen__2 ) )
           => ~ ( ~ eigen__1
               => ( X1 != eigen__3 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__5])]) ).

thf(sP1,plain,
    ( sP1
  <=> eigen__1 ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: $i] :
        ( ( in @ X1 @ eigen__0 )
       => ( singleton
          @ ( dsetconstr @ eigen__0
            @ ^ [X2: $i] : ( X2 = X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( in @ eigen__2 @ eigen__0 )
     => sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: $i,X2: $o,X3: $i] :
        ( ( in @ X3 @ X1 )
       => ! [X4: $i] :
            ( ( in @ X4 @ X1 )
           => ( X2
             => ( in @ X3
                @ ( dsetconstr @ X1
                  @ ^ [X5: $i] :
                      ( ( X2
                       => ( X5 != X3 ) )
                     => ~ ( ~ X2
                         => ( X5 != X4 ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( singleton
      @ ( dsetconstr @ eigen__0
        @ ^ [X1: $i] : ( X1 = eigen__2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( in @ eigen__2
      @ ( dsetconstr @ eigen__0
        @ ^ [X1: $i] :
            ( ( sP1
             => ( X1 != eigen__2 ) )
           => ~ ( ~ sP1
               => ( X1 != eigen__3 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( in @ eigen__2 @ eigen__0 )
     => ! [X1: $i] :
          ( ( in @ X1 @ eigen__0 )
         => ( in @ eigen__2
            @ ( dsetconstr @ eigen__0
              @ ^ [X2: $i] : ( X2 = eigen__2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ( sP1
       => ( eigen__5 != eigen__2 ) )
     => ~ ( ~ sP1
         => ( eigen__5 != eigen__3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

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

thf(sP10,plain,
    ( sP10
  <=> ( ( ^ [X1: $i] : ( X1 = eigen__2 ) )
      = ( ^ [X1: $i] :
            ( ( sP1
             => ( X1 != eigen__2 ) )
           => ~ ( ~ sP1
               => ( X1 != eigen__3 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( singleton
      @ ( dsetconstr @ eigen__0
        @ ^ [X1: $i] :
            ( ( sP1
             => ( X1 != eigen__2 ) )
           => ~ ( ~ sP1
               => ( X1 != eigen__3 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( sP1
     => ( eigen__5 != eigen__2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ! [X1: $i,X2: $o,X3: $i] :
        ( ( in @ X3 @ X1 )
       => ! [X4: $i] :
            ( ( in @ X4 @ X1 )
           => ( singleton
              @ ( dsetconstr @ X1
                @ ^ [X5: $i] :
                    ( ( X2
                     => ( X5 != X3 ) )
                   => ~ ( ~ X2
                       => ( X5 != X4 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( ( in @ eigen__2 @ eigen__0 )
     => ( in @ eigen__2
        @ ( dsetconstr @ eigen__0
          @ ^ [X1: $i] : ( X1 = eigen__2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ! [X1: $i] :
        ( ( in @ X1 @ eigen__0 )
       => sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( ( in @ eigen__2 @ eigen__0 )
     => sP5 ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ! [X1: $o,X2: $i] :
        ( ( in @ X2 @ eigen__0 )
       => ! [X3: $i] :
            ( ( in @ X3 @ eigen__0 )
           => ( singleton
              @ ( dsetconstr @ eigen__0
                @ ^ [X4: $i] :
                    ( ( X1
                     => ( X4 != X2 ) )
                   => ~ ( ~ X1
                       => ( X4 != X3 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ! [X1: $i] :
        ( ( X1 = eigen__2 )
        = ( ( sP1
           => ( X1 != eigen__2 ) )
         => ~ ( ~ sP1
             => ( X1 != eigen__3 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ( in @ eigen__2
      @ ( dsetconstr @ eigen__0
        @ ^ [X1: $i] : ( X1 = eigen__2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ( eigen__5 = eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

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

thf(sP23,plain,
    ( sP23
  <=> ( ( setunion
        @ ( dsetconstr @ eigen__0
          @ ^ [X1: $i] :
              ( ( sP1
               => ( X1 != eigen__2 ) )
             => ~ ( ~ sP1
                 => ( X1 != eigen__3 ) ) ) ) )
      = eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> ! [X1: $i] :
        ( ( in @ X1 @ eigen__0 )
       => sP20 ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ( ~ sP1
     => ( eigen__5 != eigen__3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
    ( sP26
  <=> ( sP11
     => ! [X1: $i] :
          ( ( in @ X1
            @ ( dsetconstr @ eigen__0
              @ ^ [X2: $i] :
                  ( ( sP1
                   => ( X2 != eigen__2 ) )
                 => ~ ( ~ sP1
                     => ( X2 != eigen__3 ) ) ) ) )
         => ( ( setunion
              @ ( dsetconstr @ eigen__0
                @ ^ [X2: $i] :
                    ( ( sP1
                     => ( X2 != eigen__2 ) )
                   => ~ ( ~ sP1
                       => ( X2 != eigen__3 ) ) ) ) )
            = X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
    ( sP27
  <=> ! [X1: $o,X2: $i] :
        ( ( in @ X2 @ eigen__0 )
       => ! [X3: $i] :
            ( ( in @ X3 @ eigen__0 )
           => ( X1
             => ( in @ X2
                @ ( dsetconstr @ eigen__0
                  @ ^ [X4: $i] :
                      ( ( X1
                       => ( X4 != X2 ) )
                     => ~ ( ~ X1
                         => ( X4 != X3 ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP27])]) ).

thf(sP28,plain,
    ( sP28
  <=> ( sP21 = sP8 ) ),
    introduced(definition,[new_symbols(definition,[sP28])]) ).

thf(sP29,plain,
    ( sP29
  <=> ! [X1: $i] :
        ( ( in @ X1
          @ ( dsetconstr @ eigen__0
            @ ^ [X2: $i] :
                ( ( sP1
                 => ( X2 != eigen__2 ) )
               => ~ ( ~ sP1
                   => ( X2 != eigen__3 ) ) ) ) )
       => ( ( setunion
            @ ( dsetconstr @ eigen__0
              @ ^ [X2: $i] :
                  ( ( sP1
                   => ( X2 != eigen__2 ) )
                 => ~ ( ~ sP1
                     => ( X2 != eigen__3 ) ) ) ) )
          = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP29])]) ).

thf(sP30,plain,
    ( sP30
  <=> ( in @ eigen__2 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP30])]) ).

thf(sP31,plain,
    ( sP31
  <=> ( sP6
     => sP23 ) ),
    introduced(definition,[new_symbols(definition,[sP31])]) ).

thf(sP32,plain,
    ( sP32
  <=> ( ( dsetconstr @ eigen__0
        @ ^ [X1: $i] : ( X1 = eigen__2 ) )
      = ( dsetconstr @ eigen__0
        @ ^ [X1: $i] :
            ( ( sP1
             => ( X1 != eigen__2 ) )
           => ~ ( ~ sP1
               => ( X1 != eigen__3 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP32])]) ).

thf(def_iftrueProp1,definition,
    ( iftrueProp1
    = ( ! [X1: $i,X2: $o,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
                @ ( in @ X3
                  @ ( dsetconstr @ X1
                    @ ^ [X5: $i] :
                        ( ( X2
                          & ( X5 = X3 ) )
                        | ( ( (~) @ X2 )
                          & ( X5 = X4 ) ) ) ) ) ) ) ) ) ) ).

thf(def_ifSingleton,definition,
    ( ifSingleton
    = ( ! [X1: $i,X2: $o,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ X1 )
          @ ! [X4: $i] :
              ( ^ [X5: $o,X6: $o] :
                  ( X5
                 => X6 )
              @ ( in @ X4 @ X1 )
              @ ( singleton
                @ ( dsetconstr @ X1
                  @ ^ [X5: $i] :
                      ( ( X2
                        & ( X5 = X3 ) )
                      | ( ( (~) @ X2 )
                        & ( X5 = X4 ) ) ) ) ) ) ) ) ) ).

thf(def_if,definition,
    ( if
    = ( ^ [X1: $i,X2: $o,X3: $i,X4: $i] :
          ( setunion
          @ ( dsetconstr @ X1
            @ ^ [X5: $i] :
                ( ( X2
                  & ( X5 = X3 ) )
                | ( ( (~) @ X2 )
                  & ( X5 = X4 ) ) ) ) ) ) ) ).

thf(def_theeq,definition,
    ( theeq
    = ( ! [X1: $i] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ( singleton @ X1 )
          @ ! [X2: $i] :
              ( ^ [X3: $o,X4: $o] :
                  ( X3
                 => X4 )
              @ ( in @ X2 @ X1 )
              @ ( ( setunion @ X1 )
                = X2 ) ) ) ) ) ).

thf(iftrue,conjecture,
    ( sP4
   => ( sP13
     => ( sP9
       => ! [X1: $i,X2: $o,X3: $i] :
            ( ( in @ X3 @ X1 )
           => ! [X4: $i] :
                ( ( in @ X4 @ X1 )
               => ( X2
                 => ( ( setunion
                      @ ( dsetconstr @ X1
                        @ ^ [X5: $i] :
                            ( ( X2
                             => ( X5 != X3 ) )
                           => ~ ( ~ X2
                               => ( X5 != X4 ) ) ) ) )
                    = X3 ) ) ) ) ) ) ) ).

thf(h1,negated_conjecture,
    ~ ( sP4
     => ( sP13
       => ( sP9
         => ! [X1: $i,X2: $o,X3: $i] :
              ( ( in @ X3 @ X1 )
             => ! [X4: $i] :
                  ( ( in @ X4 @ X1 )
                 => ( X2
                   => ( ( setunion
                        @ ( dsetconstr @ X1
                          @ ^ [X5: $i] :
                              ( ( X2
                               => ( X5 != X3 ) )
                             => ~ ( ~ X2
                                 => ( X5 != X4 ) ) ) ) )
                      = X3 ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[iftrue]) ).

thf(h2,assumption,
    sP4,
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ( sP13
     => ( sP9
       => ! [X1: $i,X2: $o,X3: $i] :
            ( ( in @ X3 @ X1 )
           => ! [X4: $i] :
                ( ( in @ X4 @ X1 )
               => ( X2
                 => ( ( setunion
                      @ ( dsetconstr @ X1
                        @ ^ [X5: $i] :
                            ( ( X2
                             => ( X5 != X3 ) )
                           => ~ ( ~ X2
                               => ( X5 != X4 ) ) ) ) )
                    = X3 ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP13,
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ ( sP9
     => ! [X1: $i,X2: $o,X3: $i] :
          ( ( in @ X3 @ X1 )
         => ! [X4: $i] :
              ( ( in @ X4 @ X1 )
             => ( X2
               => ( ( setunion
                    @ ( dsetconstr @ X1
                      @ ^ [X5: $i] :
                          ( ( X2
                           => ( X5 != X3 ) )
                         => ~ ( ~ X2
                             => ( X5 != X4 ) ) ) ) )
                  = X3 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    sP9,
    introduced(assumption,[]) ).

thf(h7,assumption,
    ~ ! [X1: $i,X2: $o,X3: $i] :
        ( ( in @ X3 @ X1 )
       => ! [X4: $i] :
            ( ( in @ X4 @ X1 )
           => ( X2
             => ( ( setunion
                  @ ( dsetconstr @ X1
                    @ ^ [X5: $i] :
                        ( ( X2
                         => ( X5 != X3 ) )
                       => ~ ( ~ X2
                           => ( X5 != X4 ) ) ) ) )
                = X3 ) ) ) ),
    introduced(assumption,[]) ).

thf(h8,assumption,
    ~ ! [X1: $o,X2: $i] :
        ( ( in @ X2 @ eigen__0 )
       => ! [X3: $i] :
            ( ( in @ X3 @ eigen__0 )
           => ( X1
             => ( ( setunion
                  @ ( dsetconstr @ eigen__0
                    @ ^ [X4: $i] :
                        ( ( X1
                         => ( X4 != X2 ) )
                       => ~ ( ~ X1
                           => ( X4 != X3 ) ) ) ) )
                = X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ ! [X1: $i] :
        ( ( in @ X1 @ eigen__0 )
       => ! [X2: $i] :
            ( ( in @ X2 @ eigen__0 )
           => ( sP1
             => ( ( setunion
                  @ ( dsetconstr @ eigen__0
                    @ ^ [X3: $i] :
                        ( ( sP1
                         => ( X3 != X1 ) )
                       => ~ ( ~ sP1
                           => ( X3 != X2 ) ) ) ) )
                = X1 ) ) ) ),
    introduced(assumption,[]) ).

thf(h10,assumption,
    ~ ( sP30
     => ! [X1: $i] :
          ( ( in @ X1 @ eigen__0 )
         => ( sP1
           => ( ( setunion
                @ ( dsetconstr @ eigen__0
                  @ ^ [X2: $i] :
                      ( ( sP1
                       => ( X2 != eigen__2 ) )
                     => ~ ( ~ sP1
                         => ( X2 != X1 ) ) ) ) )
              = eigen__2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h11,assumption,
    sP30,
    introduced(assumption,[]) ).

thf(h12,assumption,
    ~ ! [X1: $i] :
        ( ( in @ X1 @ eigen__0 )
       => ( sP1
         => ( ( setunion
              @ ( dsetconstr @ eigen__0
                @ ^ [X2: $i] :
                    ( ( sP1
                     => ( X2 != eigen__2 ) )
                   => ~ ( ~ sP1
                       => ( X2 != X1 ) ) ) ) )
            = eigen__2 ) ) ),
    introduced(assumption,[]) ).

thf(h13,assumption,
    ~ ( ( in @ eigen__3 @ eigen__0 )
     => ( sP1
       => sP23 ) ),
    introduced(assumption,[]) ).

thf(h14,assumption,
    in @ eigen__3 @ eigen__0,
    introduced(assumption,[]) ).

thf(h15,assumption,
    ~ ( sP1
     => sP23 ),
    introduced(assumption,[]) ).

thf(h16,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h17,assumption,
    ~ sP23,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP20
    | sP6
    | ~ sP32
    | sP15 ),
    inference(mating_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP12
    | ~ sP1
    | ~ sP21 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP8
    | sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( sP25
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( sP12
    | sP21 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP8
    | ~ sP12
    | ~ sP25 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( sP28
    | ~ sP21
    | ~ sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP28
    | sP21
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( sP19
    | ~ sP28 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).

thf(10,plain,
    ( sP10
    | ~ sP19 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( sP32
    | ~ sP10
    | sP15 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP5
    | sP11
    | ~ sP32 ),
    inference(mating_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP31
    | ~ sP6
    | sP23 ),
    inference(prop_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP29
    | sP31 ),
    inference(all_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP26
    | ~ sP11
    | sP29 ),
    inference(prop_rule,[status(thm)],]) ).

thf(16,plain,
    ( ~ sP9
    | sP26 ),
    inference(all_rule,[status(thm)],]) ).

thf(17,plain,
    ( ~ sP14
    | ~ sP30
    | sP20 ),
    inference(prop_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP24
    | sP14 ),
    inference(all_rule,[status(thm)],]) ).

thf(19,plain,
    ( ~ sP7
    | ~ sP30
    | sP24 ),
    inference(prop_rule,[status(thm)],]) ).

thf(20,plain,
    ( ~ sP3
    | ~ sP30
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(21,plain,
    ( ~ sP17
    | ~ sP30
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(22,plain,
    ( ~ sP22
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(23,plain,
    ( ~ sP16
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(24,plain,
    ( ~ sP2
    | sP17 ),
    inference(all_rule,[status(thm)],]) ).

thf(25,plain,
    ~ sP15,
    inference(prop_rule,[status(thm)],]) ).

thf(26,plain,
    ( ~ sP18
    | sP16 ),
    inference(all_rule,[status(thm)],]) ).

thf(27,plain,
    ( ~ sP27
    | sP22 ),
    inference(all_rule,[status(thm)],]) ).

thf(28,plain,
    ( ~ sP13
    | sP18 ),
    inference(all_rule,[status(thm)],]) ).

thf(29,plain,
    ( ~ sP4
    | sP27 ),
    inference(all_rule,[status(thm)],]) ).

thf(30,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h16,h17,h14,h15,h13,h11,h12,h10,h9,h8,h6,h7,h4,h5,h2,h3,h1,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,h2,h4,h6,h11,h16,h17]) ).

thf(31,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h14,h15,h13,h11,h12,h10,h9,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,30,h16,h17]) ).

thf(32,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h13,h11,h12,h10,h9,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h13,31,h14,h15]) ).

thf(33,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h11,h12,h10,h9,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__3)],[h12,32,h13]) ).

thf(34,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h10,h9,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,33,h11,h12]) ).

thf(35,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h9,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__2)],[h9,34,h10]) ).

thf(36,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__1)],[h8,35,h9]) ).

thf(37,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__0)],[h7,36,h8]) ).

thf(38,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,37,h6,h7]) ).

thf(39,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,38,h4,h5]) ).

thf(40,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,39,h2,h3]) ).

thf(41,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[40,h0]) ).

thf(0,theorem,
    ( sP4
   => ( sP13
     => ( sP9
       => ! [X1: $i,X2: $o,X3: $i] :
            ( ( in @ X3 @ X1 )
           => ! [X4: $i] :
                ( ( in @ X4 @ X1 )
               => ( X2
                 => ( ( setunion
                      @ ( dsetconstr @ X1
                        @ ^ [X5: $i] :
                            ( ( X2
                             => ( X5 != X3 ) )
                           => ~ ( ~ X2
                               => ( X5 != X4 ) ) ) ) )
                    = X3 ) ) ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h1])],[40,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU707^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34  % Computer : n009.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 Aug 23 20:30:51 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.20/0.73  % SZS status Theorem
% 0.20/0.73  % Mode: cade22grackle2xfee4
% 0.20/0.73  % Steps: 5993
% 0.20/0.73  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------