TSTP Solution File: SEU820^2 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEU820^2 : 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 : n005.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 14:09:34 EDT 2022

% Result   : Theorem 0.21s 0.40s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
    eigen__6: $i ).

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

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

thf(ty_eigen__7,type,
    eigen__7: $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_emptyset,type,
    emptyset: $i ).

thf(ty_eigen__5,type,
    eigen__5: $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
  <=> ( in @ eigen__0 @ emptyset ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( in @ eigen__7 @ ( powerset @ emptyset ) )
     => ( subset @ eigen__7 @ emptyset ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( in @ eigen__4 @ emptyset ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: $i > $o,X2: $i] :
        ( ( in @ X2 @ emptyset )
       => ( X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( in @ eigen__7 @ ( powerset @ emptyset ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( eigen__7 = emptyset ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( in @ eigen__1 @ emptyset ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: $i] :
        ~ ( in @ X1 @ emptyset ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( in @ eigen__6 @ emptyset ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ! [X1: $i,X2: $i] :
        ( ( in @ X2 @ ( powerset @ X1 ) )
       => ( subset @ X2 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( subset @ eigen__7 @ emptyset ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ! [X1: $i] :
        ( ( in @ X1 @ ( powerset @ emptyset ) )
       => ( subset @ X1 @ emptyset ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( sP11
     => sP6 ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ! [X1: $i] :
        ( ( subset @ X1 @ emptyset )
       => ( X1 = emptyset ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

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

thf(def_vacuousDall,definition,
    vacuousDall = sP4 ).

thf(def_subsetemptysetimpeq,definition,
    subsetemptysetimpeq = sP14 ).

thf(def_powersetE1,definition,
    powersetE1 = sP10 ).

thf(def_transitiveset,definition,
    ( transitiveset
    = ( ^ [X1: $i] :
        ! [X2: $i] :
          ( ( in @ X2 @ X1 )
         => ( subset @ X2 @ X1 ) ) ) ) ).

thf(def_stricttotalorderedByIn,definition,
    ( stricttotalorderedByIn
    = ( ^ [X1: $i] :
          ~ ( ~ ( ! [X2: $i] :
                    ( ( in @ X2 @ X1 )
                   => ! [X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ! [X4: $i] :
                            ( ( in @ X4 @ X1 )
                           => ( ~ ( ( in @ X2 @ X3 )
                                 => ~ ( in @ X3 @ X4 ) )
                             => ( in @ X2 @ X4 ) ) ) ) )
               => ~ ! [X2: $i] :
                      ( ( in @ X2 @ X1 )
                     => ! [X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ( ~ ( ( X2 != X3 )
                               => ( in @ X2 @ X3 ) )
                           => ( in @ X3 @ X2 ) ) ) ) )
           => ~ ! [X2: $i] :
                  ( ( in @ X2 @ X1 )
                 => ~ ( in @ X2 @ X2 ) ) ) ) ) ).

thf(def_wellorderedByIn,definition,
    ( wellorderedByIn
    = ( ^ [X1: $i] :
          ~ ( ( stricttotalorderedByIn @ X1 )
           => ~ ! [X2: $i] :
                  ( ( in @ X2 @ ( powerset @ X1 ) )
                 => ( ( nonempty @ X2 )
                   => ~ ! [X3: $i] :
                          ( ( in @ X3 @ X2 )
                         => ~ ! [X4: $i] :
                                ( ( in @ X4 @ X2 )
                               => ( ( X3 != X4 )
                                 => ( in @ X3 @ X4 ) ) ) ) ) ) ) ) ) ).

thf(def_ordinal,definition,
    ( ordinal
    = ( ^ [X1: $i] :
          ~ ( ( transitiveset @ X1 )
           => ~ ( wellorderedByIn @ X1 ) ) ) ) ).

thf(emptysetOrdinal,conjecture,
    ( sP4
   => ( sP14
     => ( sP10
       => ~ ( ! [X1: $i] :
                ( ( in @ X1 @ emptyset )
               => ( subset @ X1 @ emptyset ) )
           => ~ ~ ( ~ ( ~ ( ! [X1: $i] :
                              ( ( in @ X1 @ emptyset )
                             => ! [X2: $i] :
                                  ( ( in @ X2 @ emptyset )
                                 => ! [X3: $i] :
                                      ( ( in @ X3 @ emptyset )
                                     => ( ~ ( ( in @ X1 @ X2 )
                                           => ~ ( in @ X2 @ X3 ) )
                                       => ( in @ X1 @ X3 ) ) ) ) )
                         => ~ ! [X1: $i] :
                                ( ( in @ X1 @ emptyset )
                               => ! [X2: $i] :
                                    ( ( in @ X2 @ emptyset )
                                   => ( ~ ( ( X1 != X2 )
                                         => ( in @ X1 @ X2 ) )
                                     => ( in @ X2 @ X1 ) ) ) ) )
                     => ~ ! [X1: $i] :
                            ( ( in @ X1 @ emptyset )
                           => ~ ( in @ X1 @ X1 ) ) )
                 => ~ ! [X1: $i] :
                        ( ( in @ X1 @ ( powerset @ emptyset ) )
                       => ( ( X1 != emptyset )
                         => ~ ! [X2: $i] :
                                ( ( in @ X2 @ X1 )
                               => ~ ! [X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ( ( X2 != X3 )
                                       => ( in @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ( sP4
     => ( sP14
       => ( sP10
         => ~ ( ! [X1: $i] :
                  ( ( in @ X1 @ emptyset )
                 => ( subset @ X1 @ emptyset ) )
             => ( ~ ( ~ ( ! [X1: $i] :
                            ( ( in @ X1 @ emptyset )
                           => ! [X2: $i] :
                                ( ( in @ X2 @ emptyset )
                               => ! [X3: $i] :
                                    ( ( in @ X3 @ emptyset )
                                   => ( ~ ( ( in @ X1 @ X2 )
                                         => ~ ( in @ X2 @ X3 ) )
                                     => ( in @ X1 @ X3 ) ) ) ) )
                       => ~ ! [X1: $i] :
                              ( ( in @ X1 @ emptyset )
                             => ! [X2: $i] :
                                  ( ( in @ X2 @ emptyset )
                                 => ( ~ ( ( X1 != X2 )
                                       => ( in @ X1 @ X2 ) )
                                   => ( in @ X2 @ X1 ) ) ) ) )
                   => ~ ! [X1: $i] :
                          ( ( in @ X1 @ emptyset )
                         => ~ ( in @ X1 @ X1 ) ) )
               => ~ ! [X1: $i] :
                      ( ( in @ X1 @ ( powerset @ emptyset ) )
                     => ( ( X1 != emptyset )
                       => ~ ! [X2: $i] :
                              ( ( in @ X2 @ X1 )
                             => ~ ! [X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ( ( X2 != X3 )
                                     => ( in @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[emptysetOrdinal]) ).

thf(h1,assumption,
    sP4,
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ( sP14
     => ( sP10
       => ~ ( ! [X1: $i] :
                ( ( in @ X1 @ emptyset )
               => ( subset @ X1 @ emptyset ) )
           => ( ~ ( ~ ( ! [X1: $i] :
                          ( ( in @ X1 @ emptyset )
                         => ! [X2: $i] :
                              ( ( in @ X2 @ emptyset )
                             => ! [X3: $i] :
                                  ( ( in @ X3 @ emptyset )
                                 => ( ~ ( ( in @ X1 @ X2 )
                                       => ~ ( in @ X2 @ X3 ) )
                                   => ( in @ X1 @ X3 ) ) ) ) )
                     => ~ ! [X1: $i] :
                            ( ( in @ X1 @ emptyset )
                           => ! [X2: $i] :
                                ( ( in @ X2 @ emptyset )
                               => ( ~ ( ( X1 != X2 )
                                     => ( in @ X1 @ X2 ) )
                                 => ( in @ X2 @ X1 ) ) ) ) )
                 => ~ ! [X1: $i] :
                        ( ( in @ X1 @ emptyset )
                       => ~ ( in @ X1 @ X1 ) ) )
             => ~ ! [X1: $i] :
                    ( ( in @ X1 @ ( powerset @ emptyset ) )
                   => ( ( X1 != emptyset )
                     => ~ ! [X2: $i] :
                            ( ( in @ X2 @ X1 )
                           => ~ ! [X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ( ( X2 != X3 )
                                   => ( in @ X2 @ X3 ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    sP14,
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ( sP10
     => ~ ( ! [X1: $i] :
              ( ( in @ X1 @ emptyset )
             => ( subset @ X1 @ emptyset ) )
         => ( ~ ( ~ ( ! [X1: $i] :
                        ( ( in @ X1 @ emptyset )
                       => ! [X2: $i] :
                            ( ( in @ X2 @ emptyset )
                           => ! [X3: $i] :
                                ( ( in @ X3 @ emptyset )
                               => ( ~ ( ( in @ X1 @ X2 )
                                     => ~ ( in @ X2 @ X3 ) )
                                 => ( in @ X1 @ X3 ) ) ) ) )
                   => ~ ! [X1: $i] :
                          ( ( in @ X1 @ emptyset )
                         => ! [X2: $i] :
                              ( ( in @ X2 @ emptyset )
                             => ( ~ ( ( X1 != X2 )
                                   => ( in @ X1 @ X2 ) )
                               => ( in @ X2 @ X1 ) ) ) ) )
               => ~ ! [X1: $i] :
                      ( ( in @ X1 @ emptyset )
                     => ~ ( in @ X1 @ X1 ) ) )
           => ~ ! [X1: $i] :
                  ( ( in @ X1 @ ( powerset @ emptyset ) )
                 => ( ( X1 != emptyset )
                   => ~ ! [X2: $i] :
                          ( ( in @ X2 @ X1 )
                         => ~ ! [X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ( ( X2 != X3 )
                                 => ( in @ X2 @ X3 ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    sP10,
    introduced(assumption,[]) ).

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

thf(h7,assumption,
    ~ ! [X1: $i] :
        ( ( in @ X1 @ emptyset )
       => ( subset @ X1 @ emptyset ) ),
    introduced(assumption,[]) ).

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

thf(h9,assumption,
    ~ ( sP1
     => ( subset @ eigen__0 @ emptyset ) ),
    introduced(assumption,[]) ).

thf(h10,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h11,assumption,
    ~ ( subset @ eigen__0 @ emptyset ),
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP8
    | ~ sP1 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP4
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h10,h11,h9,h7,h5,h6,h3,h4,h1,h2,h0])],[1,2,h1,h10]) ).

thf(4,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h10,h11])],[h9,3,h10,h11]) ).

thf(5,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__0)],[h7,4,h9]) ).

thf(h12,assumption,
    ( ~ ( ! [X1: $i] :
            ( ( in @ X1 @ emptyset )
           => ! [X2: $i] :
                ( ( in @ X2 @ emptyset )
               => ! [X3: $i] :
                    ( ( in @ X3 @ emptyset )
                   => ( ~ ( ( in @ X1 @ X2 )
                         => ~ ( in @ X2 @ X3 ) )
                     => ( in @ X1 @ X3 ) ) ) ) )
       => ~ ! [X1: $i] :
              ( ( in @ X1 @ emptyset )
             => ! [X2: $i] :
                  ( ( in @ X2 @ emptyset )
                 => ( ~ ( ( X1 != X2 )
                       => ( in @ X1 @ X2 ) )
                   => ( in @ X2 @ X1 ) ) ) ) )
   => ~ ! [X1: $i] :
          ( ( in @ X1 @ emptyset )
         => ~ ( in @ X1 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h13,assumption,
    ~ ! [X1: $i] :
        ( ( in @ X1 @ ( powerset @ emptyset ) )
       => ( ( X1 != emptyset )
         => ~ ! [X2: $i] :
                ( ( in @ X2 @ X1 )
               => ~ ! [X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ( ( X2 != X3 )
                       => ( in @ X2 @ X3 ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h14,assumption,
    ( ! [X1: $i] :
        ( ( in @ X1 @ emptyset )
       => ! [X2: $i] :
            ( ( in @ X2 @ emptyset )
           => ! [X3: $i] :
                ( ( in @ X3 @ emptyset )
               => ( ~ ( ( in @ X1 @ X2 )
                     => ~ ( in @ X2 @ X3 ) )
                 => ( in @ X1 @ X3 ) ) ) ) )
   => ~ ! [X1: $i] :
          ( ( in @ X1 @ emptyset )
         => ! [X2: $i] :
              ( ( in @ X2 @ emptyset )
             => ( ~ ( ( X1 != X2 )
                   => ( in @ X1 @ X2 ) )
               => ( in @ X2 @ X1 ) ) ) ) ),
    introduced(assumption,[]) ).

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

thf(h16,assumption,
    ~ ! [X1: $i] :
        ( ( in @ X1 @ emptyset )
       => ! [X2: $i] :
            ( ( in @ X2 @ emptyset )
           => ! [X3: $i] :
                ( ( in @ X3 @ emptyset )
               => ( ~ ( ( in @ X1 @ X2 )
                     => ~ ( in @ X2 @ X3 ) )
                 => ( in @ X1 @ X3 ) ) ) ) ),
    introduced(assumption,[]) ).

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

thf(h18,assumption,
    ~ ( sP7
     => ! [X1: $i] :
          ( ( in @ X1 @ emptyset )
         => ! [X2: $i] :
              ( ( in @ X2 @ emptyset )
             => ( ~ ( ( in @ eigen__1 @ X1 )
                   => ~ ( in @ X1 @ X2 ) )
               => ( in @ eigen__1 @ X2 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h19,assumption,
    sP7,
    introduced(assumption,[]) ).

thf(h20,assumption,
    ~ ! [X1: $i] :
        ( ( in @ X1 @ emptyset )
       => ! [X2: $i] :
            ( ( in @ X2 @ emptyset )
           => ( ~ ( ( in @ eigen__1 @ X1 )
                 => ~ ( in @ X1 @ X2 ) )
             => ( in @ eigen__1 @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h21,assumption,
    ~ ( ( in @ eigen__2 @ emptyset )
     => ! [X1: $i] :
          ( ( in @ X1 @ emptyset )
         => ( ~ ( ( in @ eigen__1 @ eigen__2 )
               => ~ ( in @ eigen__2 @ X1 ) )
           => ( in @ eigen__1 @ X1 ) ) ) ),
    introduced(assumption,[]) ).

thf(h22,assumption,
    in @ eigen__2 @ emptyset,
    introduced(assumption,[]) ).

thf(h23,assumption,
    ~ ! [X1: $i] :
        ( ( in @ X1 @ emptyset )
       => ( ~ ( ( in @ eigen__1 @ eigen__2 )
             => ~ ( in @ eigen__2 @ X1 ) )
         => ( in @ eigen__1 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h24,assumption,
    ~ ( ( in @ eigen__3 @ emptyset )
     => ( ~ ( ( in @ eigen__1 @ eigen__2 )
           => ~ ( in @ eigen__2 @ eigen__3 ) )
       => ( in @ eigen__1 @ eigen__3 ) ) ),
    introduced(assumption,[]) ).

thf(h25,assumption,
    in @ eigen__3 @ emptyset,
    introduced(assumption,[]) ).

thf(h26,assumption,
    ~ ( ~ ( ( in @ eigen__1 @ eigen__2 )
         => ~ ( in @ eigen__2 @ eigen__3 ) )
     => ( in @ eigen__1 @ eigen__3 ) ),
    introduced(assumption,[]) ).

thf(h27,assumption,
    ~ ( ( in @ eigen__1 @ eigen__2 )
     => ~ ( in @ eigen__2 @ eigen__3 ) ),
    introduced(assumption,[]) ).

thf(h28,assumption,
    ~ ( in @ eigen__1 @ eigen__3 ),
    introduced(assumption,[]) ).

thf(h29,assumption,
    in @ eigen__1 @ eigen__2,
    introduced(assumption,[]) ).

thf(h30,assumption,
    in @ eigen__2 @ eigen__3,
    introduced(assumption,[]) ).

thf(6,plain,
    ( ~ sP8
    | ~ sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP4
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h29,h30,h27,h28,h25,h26,h24,h22,h23,h21,h19,h20,h18,h16,h14,h12,h8,h5,h6,h3,h4,h1,h2,h0])],[6,7,h1,h19]) ).

thf(9,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h27,h28,h25,h26,h24,h22,h23,h21,h19,h20,h18,h16,h14,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h29,h30])],[h27,8,h29,h30]) ).

thf(10,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h25,h26,h24,h22,h23,h21,h19,h20,h18,h16,h14,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h27,h28])],[h26,9,h27,h28]) ).

thf(11,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h24,h22,h23,h21,h19,h20,h18,h16,h14,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h25,h26])],[h24,10,h25,h26]) ).

thf(12,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h22,h23,h21,h19,h20,h18,h16,h14,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h24]),tab_negall(eigenvar,eigen__3)],[h23,11,h24]) ).

thf(13,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h21,h19,h20,h18,h16,h14,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h22,h23])],[h21,12,h22,h23]) ).

thf(14,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h19,h20,h18,h16,h14,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h21]),tab_negall(eigenvar,eigen__2)],[h20,13,h21]) ).

thf(15,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h18,h16,h14,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h19,h20])],[h18,14,h19,h20]) ).

thf(16,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h16,h14,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__1)],[h16,15,h18]) ).

thf(h31,assumption,
    ~ ( sP3
     => ! [X1: $i] :
          ( ( in @ X1 @ emptyset )
         => ( ~ ( ( eigen__4 != X1 )
               => ( in @ eigen__4 @ X1 ) )
           => ( in @ X1 @ eigen__4 ) ) ) ),
    introduced(assumption,[]) ).

thf(h32,assumption,
    sP3,
    introduced(assumption,[]) ).

thf(h33,assumption,
    ~ ! [X1: $i] :
        ( ( in @ X1 @ emptyset )
       => ( ~ ( ( eigen__4 != X1 )
             => ( in @ eigen__4 @ X1 ) )
         => ( in @ X1 @ eigen__4 ) ) ),
    introduced(assumption,[]) ).

thf(h34,assumption,
    ~ ( ( in @ eigen__5 @ emptyset )
     => ( ~ ( ( eigen__4 != eigen__5 )
           => ( in @ eigen__4 @ eigen__5 ) )
       => ( in @ eigen__5 @ eigen__4 ) ) ),
    introduced(assumption,[]) ).

thf(h35,assumption,
    in @ eigen__5 @ emptyset,
    introduced(assumption,[]) ).

thf(h36,assumption,
    ~ ( ~ ( ( eigen__4 != eigen__5 )
         => ( in @ eigen__4 @ eigen__5 ) )
     => ( in @ eigen__5 @ eigen__4 ) ),
    introduced(assumption,[]) ).

thf(h37,assumption,
    ~ ( ( eigen__4 != eigen__5 )
     => ( in @ eigen__4 @ eigen__5 ) ),
    introduced(assumption,[]) ).

thf(h38,assumption,
    ~ ( in @ eigen__5 @ eigen__4 ),
    introduced(assumption,[]) ).

thf(h39,assumption,
    eigen__4 != eigen__5,
    introduced(assumption,[]) ).

thf(h40,assumption,
    ~ ( in @ eigen__4 @ eigen__5 ),
    introduced(assumption,[]) ).

thf(17,plain,
    ( ~ sP8
    | ~ sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP4
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(19,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h39,h40,h37,h38,h35,h36,h34,h32,h33,h31,h17,h14,h12,h8,h5,h6,h3,h4,h1,h2,h0])],[17,18,h1,h32]) ).

thf(20,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h37,h38,h35,h36,h34,h32,h33,h31,h17,h14,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h39,h40])],[h37,19,h39,h40]) ).

thf(21,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h35,h36,h34,h32,h33,h31,h17,h14,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h37,h38])],[h36,20,h37,h38]) ).

thf(22,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h34,h32,h33,h31,h17,h14,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h35,h36])],[h34,21,h35,h36]) ).

thf(23,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h32,h33,h31,h17,h14,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h34]),tab_negall(eigenvar,eigen__5)],[h33,22,h34]) ).

thf(24,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h31,h17,h14,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h32,h33])],[h31,23,h32,h33]) ).

thf(25,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h17,h14,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h31]),tab_negall(eigenvar,eigen__4)],[h17,24,h31]) ).

thf(26,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h14,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h16]),tab_imp(discharge,[h17])],[h14,16,25,h16,h17]) ).

thf(h41,assumption,
    ~ ( sP9
     => ~ ( in @ eigen__6 @ eigen__6 ) ),
    introduced(assumption,[]) ).

thf(h42,assumption,
    sP9,
    introduced(assumption,[]) ).

thf(h43,assumption,
    in @ eigen__6 @ eigen__6,
    introduced(assumption,[]) ).

thf(27,plain,
    ( ~ sP8
    | ~ sP9 ),
    inference(all_rule,[status(thm)],]) ).

thf(28,plain,
    ( ~ sP4
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(29,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h42,h43,h41,h15,h12,h8,h5,h6,h3,h4,h1,h2,h0])],[27,28,h1,h42]) ).

thf(30,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h41,h15,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h42,h43])],[h41,29,h42,h43]) ).

thf(31,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h15,h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h41]),tab_negall(eigenvar,eigen__6)],[h15,30,h41]) ).

thf(32,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h12,h8,h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h14]),tab_imp(discharge,[h15])],[h12,26,31,h14,h15]) ).

thf(h44,assumption,
    ~ ( sP5
     => ( ~ sP6
       => ~ ! [X1: $i] :
              ( ( in @ X1 @ eigen__7 )
             => ~ ! [X2: $i] :
                    ( ( in @ X2 @ eigen__7 )
                   => ( ( X1 != X2 )
                     => ( in @ X1 @ X2 ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h45,assumption,
    sP5,
    introduced(assumption,[]) ).

thf(h46,assumption,
    ~ ( ~ sP6
     => ~ ! [X1: $i] :
            ( ( in @ X1 @ eigen__7 )
           => ~ ! [X2: $i] :
                  ( ( in @ X2 @ eigen__7 )
                 => ( ( X1 != X2 )
                   => ( in @ X1 @ X2 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h47,assumption,
    ~ sP6,
    introduced(assumption,[]) ).

thf(h48,assumption,
    ! [X1: $i] :
      ( ( in @ X1 @ eigen__7 )
     => ~ ! [X2: $i] :
            ( ( in @ X2 @ eigen__7 )
           => ( ( X1 != X2 )
             => ( in @ X1 @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(33,plain,
    ( ~ sP10
    | sP12 ),
    inference(all_rule,[status(thm)],]) ).

thf(34,plain,
    ( ~ sP12
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(35,plain,
    ( ~ sP2
    | ~ sP5
    | sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(36,plain,
    ( ~ sP14
    | sP13 ),
    inference(all_rule,[status(thm)],]) ).

thf(37,plain,
    ( ~ sP13
    | ~ sP11
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(38,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h47,h48,h45,h46,h44,h13,h8,h5,h6,h3,h4,h1,h2,h0])],[33,34,35,36,37,h3,h5,h45,h47]) ).

thf(39,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h45,h46,h44,h13,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h47,h48])],[h46,38,h47,h48]) ).

thf(40,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h44,h13,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h45,h46])],[h44,39,h45,h46]) ).

thf(41,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h13,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h44]),tab_negall(eigenvar,eigen__7)],[h13,40,h44]) ).

thf(42,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h8,h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h12]),tab_imp(discharge,[h13])],[h8,32,41,h12,h13]) ).

thf(43,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h6,5,42,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,
    ( sP4
   => ( sP14
     => ( sP10
       => ~ ( ! [X1: $i] :
                ( ( in @ X1 @ emptyset )
               => ( subset @ X1 @ emptyset ) )
           => ~ ~ ( ~ ( ~ ( ! [X1: $i] :
                              ( ( in @ X1 @ emptyset )
                             => ! [X2: $i] :
                                  ( ( in @ X2 @ emptyset )
                                 => ! [X3: $i] :
                                      ( ( in @ X3 @ emptyset )
                                     => ( ~ ( ( in @ X1 @ X2 )
                                           => ~ ( in @ X2 @ X3 ) )
                                       => ( in @ X1 @ X3 ) ) ) ) )
                         => ~ ! [X1: $i] :
                                ( ( in @ X1 @ emptyset )
                               => ! [X2: $i] :
                                    ( ( in @ X2 @ emptyset )
                                   => ( ~ ( ( X1 != X2 )
                                         => ( in @ X1 @ X2 ) )
                                     => ( in @ X2 @ X1 ) ) ) ) )
                     => ~ ! [X1: $i] :
                            ( ( in @ X1 @ emptyset )
                           => ~ ( in @ X1 @ X1 ) ) )
                 => ~ ! [X1: $i] :
                        ( ( in @ X1 @ ( powerset @ emptyset ) )
                       => ( ( X1 != emptyset )
                         => ~ ! [X2: $i] :
                                ( ( in @ X2 @ X1 )
                               => ~ ! [X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ( ( X2 != X3 )
                                       => ( in @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[46,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : SEU820^2 : TPTP v8.1.0. Released v3.7.0.
% 0.04/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n005.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 : Sun Jun 19 21:52:53 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.21/0.40  % SZS status Theorem
% 0.21/0.40  % Mode: mode213
% 0.21/0.40  % Inferences: 155
% 0.21/0.40  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------