TSTP Solution File: SEU818^2 by Lash---1.13

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEU818^2 : 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 : n010.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 17:35:42 EDT 2023

% Result   : Theorem 0.19s 0.40s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_emptyset,type,
    emptyset: $i ).

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

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

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

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

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

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

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

thf(sP3,plain,
    ( sP3
  <=> ( subset @ eigen__1 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( sP1
     => sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

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

thf(def_subsetI1,definition,
    ( subsetI1
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ! [X3: $i] :
              ( ^ [X4: $o,X5: $o] :
                  ( X4
                 => X5 )
              @ ( in @ X3 @ X1 )
              @ ( in @ X3 @ X2 ) )
          @ ( subset @ X1 @ X2 ) ) ) ) ).

thf(def_transitiveset,definition,
    ( transitiveset
    = ( ^ [X1: $i] :
        ! [X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( in @ X2 @ X1 )
          @ ( subset @ X2 @ X1 ) ) ) ) ).

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

thf(def_wellorderedByIn,definition,
    ( wellorderedByIn
    = ( ^ [X1: $i] :
          ( ( stricttotalorderedByIn @ X1 )
          & ! [X2: $i] :
              ( ^ [X3: $o,X4: $o] :
                  ( X3
                 => X4 )
              @ ( in @ X2 @ ( powerset @ X1 ) )
              @ ( ^ [X3: $o,X4: $o] :
                    ( X3
                   => X4 )
                @ ( nonempty @ X2 )
                @ ? [X3: $i] :
                    ( ( in @ X3 @ X2 )
                    & ! [X4: $i] :
                        ( ^ [X5: $o,X6: $o] :
                            ( X5
                           => X6 )
                        @ ( in @ X4 @ X2 )
                        @ ( ( X3 = X4 )
                          | ( in @ X3 @ X4 ) ) ) ) ) ) ) ) ) ).

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

thf(def_ordinalTransSet,definition,
    ( ordinalTransSet
    = ( ! [X1: $i] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ( ordinal @ X1 )
          @ ! [X2: $i,X3: $i] :
              ( ^ [X4: $o,X5: $o] :
                  ( X4
                 => X5 )
              @ ( in @ X3 @ X1 )
              @ ( ^ [X4: $o,X5: $o] :
                    ( X4
                   => X5 )
                @ ( in @ X2 @ X3 )
                @ ( in @ X2 @ X1 ) ) ) ) ) ) ).

thf(ordinalTransSet1,conjecture,
    ( ! [X1: $i,X2: $i] :
        ( ! [X3: $i] :
            ( ( in @ X3 @ X1 )
           => ( in @ X3 @ X2 ) )
       => ( subset @ X1 @ X2 ) )
   => ( ! [X1: $i] :
          ( ~ ( ! [X2: $i] :
                  ( ( in @ X2 @ X1 )
                 => ( subset @ X2 @ X1 ) )
             => ( ~ ( ~ ( ! [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 ) ) )
               => ~ ! [X2: $i] :
                      ( ( in @ X2 @ ( powerset @ X1 ) )
                     => ( ( X2 != emptyset )
                       => ~ ! [X3: $i] :
                              ( ( in @ X3 @ X2 )
                             => ~ ! [X4: $i] :
                                    ( ( in @ X4 @ X2 )
                                   => ( ( X3 != X4 )
                                     => ( in @ X3 @ X4 ) ) ) ) ) ) ) )
         => ! [X2: $i,X3: $i] :
              ( ( in @ X3 @ X1 )
             => ( ( in @ X2 @ X3 )
               => ( in @ X2 @ X1 ) ) ) )
     => ! [X1: $i] :
          ( ~ ( ! [X2: $i] :
                  ( ( in @ X2 @ X1 )
                 => ( subset @ X2 @ X1 ) )
             => ( ~ ( ~ ( ! [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 ) ) )
               => ~ ! [X2: $i] :
                      ( ( in @ X2 @ ( powerset @ X1 ) )
                     => ( ( X2 != emptyset )
                       => ~ ! [X3: $i] :
                              ( ( in @ X3 @ X2 )
                             => ~ ! [X4: $i] :
                                    ( ( in @ X4 @ X2 )
                                   => ( ( X3 != X4 )
                                     => ( in @ X3 @ X4 ) ) ) ) ) ) ) )
         => ! [X2: $i] :
              ( ( in @ X2 @ X1 )
             => ( subset @ X2 @ X1 ) ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ( ! [X1: $i,X2: $i] :
          ( ! [X3: $i] :
              ( ( in @ X3 @ X1 )
             => ( in @ X3 @ X2 ) )
         => ( subset @ X1 @ X2 ) )
     => ( ! [X1: $i] :
            ( ~ ( ! [X2: $i] :
                    ( ( in @ X2 @ X1 )
                   => ( subset @ X2 @ X1 ) )
               => ( ~ ( ~ ( ! [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 ) ) )
                 => ~ ! [X2: $i] :
                        ( ( in @ X2 @ ( powerset @ X1 ) )
                       => ( ( X2 != emptyset )
                         => ~ ! [X3: $i] :
                                ( ( in @ X3 @ X2 )
                               => ~ ! [X4: $i] :
                                      ( ( in @ X4 @ X2 )
                                     => ( ( X3 != X4 )
                                       => ( in @ X3 @ X4 ) ) ) ) ) ) ) )
           => ! [X2: $i,X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( ( in @ X2 @ X3 )
                 => ( in @ X2 @ X1 ) ) ) )
       => ! [X1: $i] :
            ( ~ ( ! [X2: $i] :
                    ( ( in @ X2 @ X1 )
                   => ( subset @ X2 @ X1 ) )
               => ( ~ ( ~ ( ! [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 ) ) )
                 => ~ ! [X2: $i] :
                        ( ( in @ X2 @ ( powerset @ X1 ) )
                       => ( ( X2 != emptyset )
                         => ~ ! [X3: $i] :
                                ( ( in @ X3 @ X2 )
                               => ~ ! [X4: $i] :
                                      ( ( in @ X4 @ X2 )
                                     => ( ( X3 != X4 )
                                       => ( in @ X3 @ X4 ) ) ) ) ) ) ) )
           => ! [X2: $i] :
                ( ( in @ X2 @ X1 )
               => ( subset @ X2 @ X1 ) ) ) ) ),
    inference(assume_negation,[status(cth)],[ordinalTransSet1]) ).

thf(h1,assumption,
    ! [X1: $i,X2: $i] :
      ( ! [X3: $i] :
          ( ( in @ X3 @ X1 )
         => ( in @ X3 @ X2 ) )
     => ( subset @ X1 @ X2 ) ),
    introduced(assumption,[]) ).

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

thf(h3,assumption,
    ! [X1: $i] :
      ( ~ ( ! [X2: $i] :
              ( ( in @ X2 @ X1 )
             => ( subset @ X2 @ X1 ) )
         => ( ~ ( ~ ( ! [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 ) ) )
           => ~ ! [X2: $i] :
                  ( ( in @ X2 @ ( powerset @ X1 ) )
                 => ( ( X2 != emptyset )
                   => ~ ! [X3: $i] :
                          ( ( in @ X3 @ X2 )
                         => ~ ! [X4: $i] :
                                ( ( in @ X4 @ X2 )
                               => ( ( X3 != X4 )
                                 => ( in @ X3 @ X4 ) ) ) ) ) ) ) )
     => ! [X2: $i,X3: $i] :
          ( ( in @ X3 @ X1 )
         => ( ( in @ X2 @ X3 )
           => ( in @ X2 @ X1 ) ) ) ),
    introduced(assumption,[]) ).

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

thf(h5,assumption,
    ~ ( ~ ( sP2
         => ( ~ ( ~ ( ! [X1: $i] :
                        ( ( in @ X1 @ eigen__0 )
                       => ! [X2: $i] :
                            ( ( in @ X2 @ eigen__0 )
                           => ! [X3: $i] :
                                ( ( in @ X3 @ eigen__0 )
                               => ( ~ ( ( in @ X1 @ X2 )
                                     => ~ ( in @ X2 @ X3 ) )
                                 => ( in @ X1 @ X3 ) ) ) ) )
                   => ~ ! [X1: $i] :
                          ( ( in @ X1 @ eigen__0 )
                         => ! [X2: $i] :
                              ( ( in @ X2 @ eigen__0 )
                             => ( ~ ( ( X1 != X2 )
                                   => ( in @ X1 @ X2 ) )
                               => ( in @ X2 @ X1 ) ) ) ) )
               => ~ ! [X1: $i] :
                      ( ( in @ X1 @ eigen__0 )
                     => ~ ( in @ X1 @ X1 ) ) )
           => ~ ! [X1: $i] :
                  ( ( in @ X1 @ ( powerset @ eigen__0 ) )
                 => ( ( X1 != emptyset )
                   => ~ ! [X2: $i] :
                          ( ( in @ X2 @ X1 )
                         => ~ ! [X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ( ( X2 != X3 )
                                 => ( in @ X2 @ X3 ) ) ) ) ) ) ) )
     => sP2 ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ ( sP2
     => ( ~ ( ~ ( ! [X1: $i] :
                    ( ( in @ X1 @ eigen__0 )
                   => ! [X2: $i] :
                        ( ( in @ X2 @ eigen__0 )
                       => ! [X3: $i] :
                            ( ( in @ X3 @ eigen__0 )
                           => ( ~ ( ( in @ X1 @ X2 )
                                 => ~ ( in @ X2 @ X3 ) )
                             => ( in @ X1 @ X3 ) ) ) ) )
               => ~ ! [X1: $i] :
                      ( ( in @ X1 @ eigen__0 )
                     => ! [X2: $i] :
                          ( ( in @ X2 @ eigen__0 )
                         => ( ~ ( ( X1 != X2 )
                               => ( in @ X1 @ X2 ) )
                           => ( in @ X2 @ X1 ) ) ) ) )
           => ~ ! [X1: $i] :
                  ( ( in @ X1 @ eigen__0 )
                 => ~ ( in @ X1 @ X1 ) ) )
       => ~ ! [X1: $i] :
              ( ( in @ X1 @ ( powerset @ eigen__0 ) )
             => ( ( X1 != emptyset )
               => ~ ! [X2: $i] :
                      ( ( in @ X2 @ X1 )
                     => ~ ! [X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ( ( X2 != X3 )
                             => ( in @ X2 @ X3 ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    ~ sP2,
    introduced(assumption,[]) ).

thf(h8,assumption,
    sP2,
    introduced(assumption,[]) ).

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

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

thf(h11,assumption,
    ! [X1: $i] :
      ( ( in @ X1 @ ( powerset @ eigen__0 ) )
     => ( ( X1 != emptyset )
       => ~ ! [X2: $i] :
              ( ( in @ X2 @ X1 )
             => ~ ! [X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ( ( X2 != X3 )
                     => ( in @ X2 @ X3 ) ) ) ) ) ),
    introduced(assumption,[]) ).

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

thf(h13,assumption,
    ! [X1: $i] :
      ( ( in @ X1 @ eigen__0 )
     => ~ ( in @ X1 @ X1 ) ),
    introduced(assumption,[]) ).

thf(h14,assumption,
    ! [X1: $i] :
      ( ( in @ X1 @ eigen__0 )
     => ! [X2: $i] :
          ( ( in @ X2 @ eigen__0 )
         => ! [X3: $i] :
              ( ( in @ X3 @ eigen__0 )
             => ( ~ ( ( in @ X1 @ X2 )
                   => ~ ( in @ X2 @ X3 ) )
               => ( in @ X1 @ X3 ) ) ) ) ),
    introduced(assumption,[]) ).

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

thf(h16,assumption,
    ~ sP4,
    introduced(assumption,[]) ).

thf(h17,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h18,assumption,
    ~ sP3,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP4
    | ~ sP1
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP2
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h17,h18,h16,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h1,h2,h0])],[1,2,h8,h17,h18]) ).

thf(4,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h16,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h17,h18])],[h16,3,h17,h18]) ).

thf(5,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__1)],[h7,4,h16]) ).

thf(6,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h14,h15])],[h12,5,h14,h15]) ).

thf(7,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h10,h11,h8,h9,h6,h7,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h12,h13])],[h10,6,h12,h13]) ).

thf(8,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h8,h9,h6,h7,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h10,h11])],[h9,7,h10,h11]) ).

thf(9,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h6,h7,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h8,h9])],[h6,8,h8,h9]) ).

thf(10,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h6,h7])],[h5,9,h6,h7]) ).

thf(11,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h4,10,h5]) ).

thf(12,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,11,h3,h4]) ).

thf(13,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,12,h1,h2]) ).

thf(0,theorem,
    ( ! [X1: $i,X2: $i] :
        ( ! [X3: $i] :
            ( ( in @ X3 @ X1 )
           => ( in @ X3 @ X2 ) )
       => ( subset @ X1 @ X2 ) )
   => ( ! [X1: $i] :
          ( ~ ( ! [X2: $i] :
                  ( ( in @ X2 @ X1 )
                 => ( subset @ X2 @ X1 ) )
             => ( ~ ( ~ ( ! [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 ) ) )
               => ~ ! [X2: $i] :
                      ( ( in @ X2 @ ( powerset @ X1 ) )
                     => ( ( X2 != emptyset )
                       => ~ ! [X3: $i] :
                              ( ( in @ X3 @ X2 )
                             => ~ ! [X4: $i] :
                                    ( ( in @ X4 @ X2 )
                                   => ( ( X3 != X4 )
                                     => ( in @ X3 @ X4 ) ) ) ) ) ) ) )
         => ! [X2: $i,X3: $i] :
              ( ( in @ X3 @ X1 )
             => ( ( in @ X2 @ X3 )
               => ( in @ X2 @ X1 ) ) ) )
     => ! [X1: $i] :
          ( ~ ( ! [X2: $i] :
                  ( ( in @ X2 @ X1 )
                 => ( subset @ X2 @ X1 ) )
             => ( ~ ( ~ ( ! [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 ) ) )
               => ~ ! [X2: $i] :
                      ( ( in @ X2 @ ( powerset @ X1 ) )
                     => ( ( X2 != emptyset )
                       => ~ ! [X3: $i] :
                              ( ( in @ X3 @ X2 )
                             => ~ ! [X4: $i] :
                                    ( ( in @ X4 @ X2 )
                                   => ( ( X3 != X4 )
                                     => ( in @ X3 @ X4 ) ) ) ) ) ) ) )
         => ! [X2: $i] :
              ( ( in @ X2 @ X1 )
             => ( subset @ X2 @ X1 ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[13,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU818^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.12  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33  % Computer : n010.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Wed Aug 23 15:26:36 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.19/0.40  % SZS status Theorem
% 0.19/0.40  % Mode: cade22grackle2xfee4
% 0.19/0.40  % Steps: 14
% 0.19/0.40  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------