TSTP Solution File: SEU492^1 by Lash---1.13

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEU492^1 : TPTP v8.1.2. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -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  : 300s
% DateTime : Thu Aug 31 17:17:53 EDT 2023

% Result   : Theorem 0.20s 0.48s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   77
% Syntax   : Number of formulae    :   90 (  53 unt;   4 typ;  32 def)
%            Number of atoms       :  216 (  41 equ;   4 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  508 (  97   ~;  25   |;  12   &; 294   @)
%                                         (  17 <=>;  63  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   98 (  98   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   54 (  51 usr;  52 con; 0-2 aty)
%            Number of variables   :  179 (  84   ^;  90   !;   5   ?; 179   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_eigen__5,type,
    eigen__5: $i ).

thf(ty_eigen__6,type,
    eigen__6: $i ).

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

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

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

thf(eigendef_eigen__1,definition,
    ( eigen__1
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ~ ( eigen__0 @ X1 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__1])]) ).

thf(eigendef_eigen__6,definition,
    ( eigen__6
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ( ( eigen__0 @ eigen__5 @ X1 )
           => ~ ( eigen__0 @ X1 @ eigen__5 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__6])]) ).

thf(eigendef_eigen__5,definition,
    ( eigen__5
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ! [X2: $i] :
              ( ( eigen__0 @ X1 @ X2 )
             => ~ ( eigen__0 @ X2 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__5])]) ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: $i,X2: $i,X3: $i] :
        ( ~ ( ( eigen__0 @ X1 @ X2 )
           => ~ ( eigen__0 @ X2 @ X3 ) )
       => ( eigen__0 @ X1 @ X3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( eigen__0 @ eigen__6 @ eigen__6 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: $i,X2: $i] :
        ( ~ ( ( eigen__0 @ eigen__6 @ X1 )
           => ~ ( eigen__0 @ X1 @ X2 ) )
       => ( eigen__0 @ eigen__6 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( eigen__0 @ eigen__1 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ~ ( ( eigen__0 @ eigen__6 @ eigen__5 )
         => ~ ( eigen__0 @ eigen__5 @ eigen__6 ) )
     => sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ( eigen__0 @ eigen__5 @ eigen__6 )
     => ~ ( eigen__0 @ eigen__6 @ eigen__5 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: $i] :
        ( ( eigen__0 @ eigen__1 @ X1 )
       => ~ ( eigen__0 @ X1 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( sP4
     => ~ sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( eigen__0 @ eigen__6 @ eigen__5 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ! [X1: $i] :
        ( ( eigen__0 @ eigen__5 @ X1 )
       => ~ ( eigen__0 @ X1 @ eigen__5 ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ! [X1: $i,X2: $i] :
        ( ( eigen__0 @ X1 @ X2 )
       => ~ ( eigen__0 @ X2 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( ! [X1: $i] :
          ~ ( eigen__0 @ X1 @ X1 )
     => ~ sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( eigen__0 @ eigen__5 @ eigen__6 ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( sP11
     => ~ sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ! [X1: $i] :
        ~ ( eigen__0 @ X1 @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( sP9
     => ~ sP13 ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ! [X1: $i] :
        ( ~ ( sP9
           => ~ ( eigen__0 @ eigen__5 @ X1 ) )
       => ( eigen__0 @ eigen__6 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(def_subrel,definition,
    ( subrel
    = ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
        ! [X3: $i,X4: $i] :
          ( ^ [X5: $o,X6: $o] :
              ( X5
             => X6 )
          @ ( X1 @ X3 @ X4 )
          @ ( X2 @ X3 @ X4 ) ) ) ) ).

thf(def_inv,definition,
    ( inv
    = ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) ).

thf(def_idem,definition,
    ( idem
    = ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
        ! [X2: $i > $i > $o] :
          ( ( X1 @ ( X1 @ X2 ) )
          = ( X1 @ X2 ) ) ) ) ).

thf(def_infl,definition,
    ( infl
    = ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
        ! [X2: $i > $i > $o] : ( subrel @ X2 @ ( X1 @ X2 ) ) ) ) ).

thf(def_mono,definition,
    ( mono
    = ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
        ! [X2: $i > $i > $o,X3: $i > $i > $o] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( subrel @ X2 @ X3 )
          @ ( subrel @ ( X1 @ X2 ) @ ( X1 @ X3 ) ) ) ) ) ).

thf(def_refl,definition,
    ( refl
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) ).

thf(def_irrefl,definition,
    ( irrefl
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i] : ( (~) @ ( X1 @ X2 @ X2 ) ) ) ) ).

thf(def_rc,definition,
    ( rc
    = ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
          ( ( X2 = X3 )
          | ( X1 @ X2 @ X3 ) ) ) ) ).

thf(def_symm,definition,
    ( symm
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( X1 @ X2 @ X3 )
          @ ( X1 @ X3 @ X2 ) ) ) ) ).

thf(def_antisymm,definition,
    ( antisymm
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( ( X1 @ X2 @ X3 )
            & ( X1 @ X3 @ X2 ) )
          @ ( X2 = X3 ) ) ) ) ).

thf(def_asymm,definition,
    ( asymm
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( X1 @ X2 @ X3 )
          @ ( (~) @ ( X1 @ X3 @ X2 ) ) ) ) ) ).

thf(def_sc,definition,
    ( sc
    = ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
          ( ( X1 @ X3 @ X2 )
          | ( X1 @ X2 @ X3 ) ) ) ) ).

thf(def_trans,definition,
    ( trans
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i,X4: $i] :
          ( ^ [X5: $o,X6: $o] :
              ( X5
             => X6 )
          @ ( ( X1 @ X2 @ X3 )
            & ( X1 @ X3 @ X4 ) )
          @ ( X1 @ X2 @ X4 ) ) ) ) ).

thf(def_tc,definition,
    ( tc
    = ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
        ! [X4: $i > $i > $o] :
          ( ^ [X5: $o,X6: $o] :
              ( X5
             => X6 )
          @ ( ( trans @ X4 )
            & ( subrel @ X1 @ X4 ) )
          @ ( X4 @ X2 @ X3 ) ) ) ) ).

thf(def_trc,definition,
    ( trc
    = ( ^ [X1: $i > $i > $o] : ( rc @ ( tc @ X1 ) ) ) ) ).

thf(def_trsc,definition,
    ( trsc
    = ( ^ [X1: $i > $i > $o] : ( sc @ ( rc @ ( tc @ X1 ) ) ) ) ) ).

thf(def_po,definition,
    ( po
    = ( ^ [X1: $i > $i > $o] :
          ( ( refl @ X1 )
          & ( antisymm @ X1 )
          & ( trans @ X1 ) ) ) ) ).

thf(def_so,definition,
    ( so
    = ( ^ [X1: $i > $i > $o] :
          ( ( asymm @ X1 )
          & ( trans @ X1 ) ) ) ) ).

thf(def_total,definition,
    ( total
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i] :
          ( ( X2 = X3 )
          | ( X1 @ X2 @ X3 )
          | ( X1 @ X3 @ X2 ) ) ) ) ).

thf(def_term,definition,
    ( term
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i > $o] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ? [X3: $i] : ( X2 @ X3 )
          @ ? [X3: $i] :
              ( ( X2 @ X3 )
              & ! [X4: $i] :
                  ( ^ [X5: $o,X6: $o] :
                      ( X5
                     => X6 )
                  @ ( X2 @ X4 )
                  @ ( (~) @ ( X1 @ X3 @ X4 ) ) ) ) ) ) ) ).

thf(def_ind,definition,
    ( ind
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i > $o] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ! [X3: $i] :
              ( ^ [X4: $o,X5: $o] :
                  ( X4
                 => X5 )
              @ ! [X4: $i] :
                  ( ^ [X5: $o,X6: $o] :
                      ( X5
                     => X6 )
                  @ ( tc @ X1 @ X3 @ X4 )
                  @ ( X2 @ X4 ) )
              @ ( X2 @ X3 ) )
          @ ! [X3: $i] : ( X2 @ X3 ) ) ) ) ).

thf(def_innf,definition,
    ( innf
    = ( ^ [X1: $i > $i > $o,X2: $i] :
          ( (~)
          @ ? [X3: $i] : ( X1 @ X2 @ X3 ) ) ) ) ).

thf(def_nfof,definition,
    ( nfof
    = ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
          ( ( trc @ X1 @ X3 @ X2 )
          & ( innf @ X1 @ X2 ) ) ) ) ).

thf(def_norm,definition,
    ( norm
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i] :
        ? [X3: $i] : ( nfof @ X1 @ X3 @ X2 ) ) ) ).

thf(def_join,definition,
    ( join
    = ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
        ? [X4: $i] :
          ( ( trc @ X1 @ X2 @ X4 )
          & ( trc @ X1 @ X3 @ X4 ) ) ) ) ).

thf(def_lconfl,definition,
    ( lconfl
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i,X4: $i] :
          ( ^ [X5: $o,X6: $o] :
              ( X5
             => X6 )
          @ ( ( X1 @ X2 @ X4 )
            & ( X1 @ X2 @ X3 ) )
          @ ( join @ X1 @ X4 @ X3 ) ) ) ) ).

thf(def_sconfl,definition,
    ( sconfl
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i,X4: $i] :
          ( ^ [X5: $o,X6: $o] :
              ( X5
             => X6 )
          @ ( ( X1 @ X2 @ X4 )
            & ( trc @ X1 @ X2 @ X3 ) )
          @ ( join @ X1 @ X4 @ X3 ) ) ) ) ).

thf(def_confl,definition,
    ( confl
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i,X4: $i] :
          ( ^ [X5: $o,X6: $o] :
              ( X5
             => X6 )
          @ ( ( trc @ X1 @ X2 @ X4 )
            & ( trc @ X1 @ X2 @ X3 ) )
          @ ( join @ X1 @ X4 @ X3 ) ) ) ) ).

thf(def_cr,definition,
    ( cr
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( trsc @ X1 @ X2 @ X3 )
          @ ( join @ X1 @ X2 @ X3 ) ) ) ) ).

thf(alternative_definition_of_strict_order,conjecture,
    ( ( ^ [X1: $i > $i > $o] :
          ~ ( ! [X2: $i,X3: $i] :
                ( ( X1 @ X2 @ X3 )
               => ~ ( X1 @ X3 @ X2 ) )
           => ~ ! [X2: $i,X3: $i,X4: $i] :
                  ( ~ ( ( X1 @ X2 @ X3 )
                     => ~ ( X1 @ X3 @ X4 ) )
                 => ( X1 @ X2 @ X4 ) ) ) )
    = ( ^ [X1: $i > $i > $o] :
          ~ ( ! [X2: $i] :
                ~ ( X1 @ X2 @ X2 )
           => ~ ! [X2: $i,X3: $i,X4: $i] :
                  ( ~ ( ( X1 @ X2 @ X3 )
                     => ~ ( X1 @ X3 @ X4 ) )
                 => ( X1 @ X2 @ X4 ) ) ) ) ) ).

thf(h1,negated_conjecture,
    ( ( ^ [X1: $i > $i > $o] :
          ~ ( ! [X2: $i,X3: $i] :
                ( ( X1 @ X2 @ X3 )
               => ~ ( X1 @ X3 @ X2 ) )
           => ~ ! [X2: $i,X3: $i,X4: $i] :
                  ( ~ ( ( X1 @ X2 @ X3 )
                     => ~ ( X1 @ X3 @ X4 ) )
                 => ( X1 @ X2 @ X4 ) ) ) )
   != ( ^ [X1: $i > $i > $o] :
          ~ ( ! [X2: $i] :
                ~ ( X1 @ X2 @ X2 )
           => ~ ! [X2: $i,X3: $i,X4: $i] :
                  ( ~ ( ( X1 @ X2 @ X3 )
                     => ~ ( X1 @ X3 @ X4 ) )
                 => ( X1 @ X2 @ X4 ) ) ) ) ),
    inference(assume_negation,[status(cth)],[alternative_definition_of_strict_order]) ).

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

thf(h3,assumption,
    ( ~ sP14 != ~ sP12 ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ sP14,
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ sP12,
    introduced(assumption,[]) ).

thf(h6,assumption,
    sP14,
    introduced(assumption,[]) ).

thf(h7,assumption,
    sP12,
    introduced(assumption,[]) ).

thf(h8,assumption,
    sP11,
    introduced(assumption,[]) ).

thf(h9,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP8
    | ~ sP4
    | ~ sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP7
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP11
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( sP15
    | sP4 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).

thf(5,plain,
    ( ~ sP12
    | ~ sP15
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h8,h9,h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,h8,h9,h5]) ).

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

thf(h10,assumption,
    sP15,
    introduced(assumption,[]) ).

thf(8,plain,
    ( ~ sP16
    | ~ sP9
    | ~ sP13 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP5
    | sP16
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP17
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP3
    | sP17 ),
    inference(all_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP15
    | ~ sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP1
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(14,plain,
    ( sP6
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(15,plain,
    ( sP6
    | sP13 ),
    inference(prop_rule,[status(thm)],]) ).

thf(16,plain,
    ( sP10
    | ~ sP6 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).

thf(17,plain,
    ( sP11
    | ~ sP10 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).

thf(18,plain,
    ( ~ sP14
    | ~ sP11
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(19,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h10,h9,h6,h7,h3,h2,h1,h0])],[8,9,10,11,12,13,14,15,16,17,18,h6,h10,h9]) ).

thf(20,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h6,h7,h3,h2,h1,h0]),tab_negimp(discharge,[h10,h9])],[h7,19,h10,h9]) ).

thf(21,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h3,h2,h1,h0]),tab_be(discharge,[h4,h5]),tab_be(discharge,[h6,h7])],[h3,7,20,h4,h5,h6,h7]) ).

thf(22,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,21,h3]) ).

thf(23,plain,
    $false,
    inference(tab_fe,[status(thm),assumptions([h1,h0]),tab_fe(discharge,[h2])],[h1,22,h2]) ).

thf(24,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[23,h0]) ).

thf(0,theorem,
    ( ( ^ [X1: $i > $i > $o] :
          ~ ( ! [X2: $i,X3: $i] :
                ( ( X1 @ X2 @ X3 )
               => ~ ( X1 @ X3 @ X2 ) )
           => ~ ! [X2: $i,X3: $i,X4: $i] :
                  ( ~ ( ( X1 @ X2 @ X3 )
                     => ~ ( X1 @ X3 @ X4 ) )
                 => ( X1 @ X2 @ X4 ) ) ) )
    = ( ^ [X1: $i > $i > $o] :
          ~ ( ! [X2: $i] :
                ~ ( X1 @ X2 @ X2 )
           => ~ ! [X2: $i,X3: $i,X4: $i] :
                  ( ~ ( ( X1 @ X2 @ X3 )
                     => ~ ( X1 @ X3 @ X4 ) )
                 => ( X1 @ X2 @ X4 ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h1])],[23,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : SEU492^1 : TPTP v8.1.2. Released v3.6.0.
% 0.12/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35  % Computer : n003.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Wed Aug 23 19:10:07 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.20/0.48  % SZS status Theorem
% 0.20/0.48  % Mode: cade22grackle2xfee4
% 0.20/0.48  % Steps: 771
% 0.20/0.48  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------