TSTP Solution File: SEU902^5 by Lash---1.13

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%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEU902^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n020.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 17:37:49 EDT 2023

% Result   : Theorem 0.20s 0.41s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   38
% Syntax   : Number of formulae    :   46 (  10 unt;   3 typ;   1 def)
%            Number of atoms       :  134 (  32 equ;   0 cnn)
%            Maximal formula atoms :    5 (   3 avg)
%            Number of connectives :  183 (  58   ~;  17   |;   0   &;  68   @)
%                                         (  15 <=>;  25  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   30 (  30   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   21 (  19 usr;  17 con; 0-2 aty)
%            Number of variables   :   28 (   5   ^;  23   !;   0   ?;  28   :)

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

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

thf(ty_d,type,
    d: $i > $o ).

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

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

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

thf(sP2,plain,
    ( sP2
  <=> ( ( ( eigen__0 @ d )
        = ( eigen__0 @ eigen__1 ) )
     => ( d = eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

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

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

thf(sP5,plain,
    ( sP5
  <=> ! [X1: $i] :
        ( ( d @ X1 )
        = ( eigen__1 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: $i > $o] :
        ( ( ( eigen__0 @ d )
          = ( eigen__0 @ X1 ) )
       => ( d = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

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

thf(sP8,plain,
    ( sP8
  <=> ( ~ sP4
     => ( ( eigen__0 @ d )
       != ( eigen__0 @ eigen__1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( ( eigen__0 @ d )
      = ( eigen__0 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( ( d @ ( eigen__0 @ d ) )
      = ( eigen__1 @ ( eigen__0 @ d ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

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

thf(sP12,plain,
    ( sP12
  <=> ( d @ ( eigen__0 @ d ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ! [X1: $i > $o] :
        ( ~ ( X1 @ ( eigen__0 @ X1 ) )
       => ( ( eigen__0 @ d )
         != ( eigen__0 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

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

thf(sP15,plain,
    ( sP15
  <=> ! [X1: $i] :
        ( ( d @ X1 )
        = ( ~ ! [X2: $i > $o] :
                ( ~ ( X2 @ ( eigen__0 @ X2 ) )
               => ( X1
                 != ( eigen__0 @ X2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(cTHM143_pme,conjecture,
    ! [X1: ( $i > $o ) > $i] :
      ( ~ ( ! [X2: $i > $o,X3: $i > $o] :
              ( ( ( X1 @ X2 )
                = ( X1 @ X3 ) )
             => ( X2 = X3 ) )
         => ( d
           != ( ^ [X2: $i] :
                  ~ ! [X3: $i > $o] :
                      ( ~ ( X3 @ ( X1 @ X3 ) )
                     => ( X2
                       != ( X1 @ X3 ) ) ) ) ) )
     => ~ ( d @ ( X1 @ d ) ) ) ).

thf(h1,negated_conjecture,
    ~ ! [X1: ( $i > $o ) > $i] :
        ( ~ ( ! [X2: $i > $o,X3: $i > $o] :
                ( ( ( X1 @ X2 )
                  = ( X1 @ X3 ) )
               => ( X2 = X3 ) )
           => ( d
             != ( ^ [X2: $i] :
                    ~ ! [X3: $i > $o] :
                        ( ~ ( X3 @ ( X1 @ X3 ) )
                       => ( X2
                         != ( X1 @ X3 ) ) ) ) ) )
       => ~ ( d @ ( X1 @ d ) ) ),
    inference(assume_negation,[status(cth)],[cTHM143_pme]) ).

thf(h2,assumption,
    ~ ( ~ ( sP11
         => ~ sP1 )
     => ~ sP12 ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ( sP11
     => ~ sP1 ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP12,
    introduced(assumption,[]) ).

thf(h5,assumption,
    sP11,
    introduced(assumption,[]) ).

thf(h6,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP14
    | sP4
    | ~ sP9 ),
    inference(mating_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP10
    | ~ sP12
    | sP14 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP5
    | sP10 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP7
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP2
    | ~ sP9
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP6
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( sP8
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP8
    | ~ sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( sP13
    | ~ sP8 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).

thf(10,plain,
    ( ~ sP3
    | ~ sP12
    | ~ sP13 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP15
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP11
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP1
    | sP15 ),
    inference(prop_rule,[status(thm)],]) ).

thf(14,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h5,h6,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,h5,h6,h4]) ).

thf(15,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h3,14,h5,h6]) ).

thf(16,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,15,h3,h4]) ).

thf(17,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,16,h2]) ).

thf(18,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[17,h0]) ).

thf(0,theorem,
    ! [X1: ( $i > $o ) > $i] :
      ( ~ ( ! [X2: $i > $o,X3: $i > $o] :
              ( ( ( X1 @ X2 )
                = ( X1 @ X3 ) )
             => ( X2 = X3 ) )
         => ( d
           != ( ^ [X2: $i] :
                  ~ ! [X3: $i > $o] :
                      ( ~ ( X3 @ ( X1 @ X3 ) )
                     => ( X2
                       != ( X1 @ X3 ) ) ) ) ) )
     => ~ ( d @ ( X1 @ d ) ) ),
    inference(contra,[status(thm),contra(discharge,[h1])],[17,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU902^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n020.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Wed Aug 23 14:48:15 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.20/0.41  % SZS status Theorem
% 0.20/0.41  % Mode: cade22grackle2xfee4
% 0.20/0.41  % Steps: 276
% 0.20/0.41  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------