TSTP Solution File: SEU861^5 by Lash---1.13

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEU861^5 : 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 : 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 17:37:41 EDT 2023

% Result   : Theorem 1.30s 1.50s
% Output   : Proof 1.30s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   49
% Syntax   : Number of formulae    :   59 (  15 unt;   6 typ;   1 def)
%            Number of atoms       :  135 (  14 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  265 (  83   ~;  19   |;   0   &;  72   @)
%                                         (  18 <=>;  73  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   36 (  36   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   26 (  24 usr;  22 con; 0-2 aty)
%            Number of variables   :   54 (   1   ^;  53   !;   0   ?;  54   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_a,type,
    a: $tType ).

thf(ty_cB,type,
    cB: a > $o ).

thf(ty_eigen__5,type,
    eigen__5: a ).

thf(ty_cC,type,
    cC: a > $o ).

thf(ty_eigen__26,type,
    eigen__26: a ).

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

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

thf(eigendef_eigen__26,definition,
    ( eigen__26
    = ( eps__0
      @ ^ [X1: a] :
          ~ ( ( cB @ X1 )
           => ( ~ ( cC @ X1 )
             => ( X1 = eigen__5 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__26])]) ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: a > $o,X2: a,X3: a > $o] :
        ( ~ ( ( eigen__0 @ X1 )
           => ~ ! [X4: a] :
                  ( ( X3 @ X4 )
                 => ( ~ ( X1 @ X4 )
                   => ( X4 = X2 ) ) ) )
       => ( eigen__0 @ X3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ! [X1: a > $o] :
          ( ! [X2: a] :
              ~ ( X1 @ X2 )
         => ( eigen__0 @ X1 ) )
     => ~ sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( eigen__0 @ cC )
     => ~ ! [X1: a] :
            ( ( cB @ X1 )
           => ( ~ ( cC @ X1 )
             => ( X1 = eigen__5 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

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

thf(sP5,plain,
    ( sP5
  <=> ( cB @ eigen__26 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: a,X2: a > $o] :
        ( ~ ( ( eigen__0 @ cC )
           => ~ ! [X3: a] :
                  ( ( X2 @ X3 )
                 => ( ~ ( cC @ X3 )
                   => ( X3 = X1 ) ) ) )
       => ( eigen__0 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( sP5
     => ( ~ ( cC @ eigen__26 )
       => ( eigen__26 = eigen__5 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( sP5
     => ( cC @ eigen__26 ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( ~ sP2
     => ( eigen__0 @ cC ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( cC @ eigen__26 ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( ~ sP3
     => ( eigen__0 @ cB ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ! [X1: a > $o] :
        ( ! [X2: a] :
            ~ ( X1 @ X2 )
       => ( eigen__0 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

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

thf(sP14,plain,
    ( sP14
  <=> ! [X1: a > $o] :
        ( ~ ( ( eigen__0 @ cC )
           => ~ ! [X2: a] :
                  ( ( X1 @ X2 )
                 => ( ~ ( cC @ X2 )
                   => ( X2 = eigen__5 ) ) ) )
       => ( eigen__0 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( eigen__0 @ cC ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( ~ sP10
     => ( eigen__26 = eigen__5 ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ! [X1: a] :
        ( ( cB @ X1 )
       => ( cC @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ! [X1: a] :
        ( ( cB @ X1 )
       => ( ~ ( cC @ X1 )
         => ( X1 = eigen__5 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(cTHM531E_pme,conjecture,
    ( ~ ( sP4
       => ~ sP17 )
   => ! [X1: ( a > $o ) > $o] :
        ( ~ ( ! [X2: a > $o] :
                ( ! [X3: a] :
                    ~ ( X2 @ X3 )
               => ( X1 @ X2 ) )
           => ~ ! [X2: a > $o,X3: a,X4: a > $o] :
                  ( ~ ( ( X1 @ X2 )
                     => ~ ! [X5: a] :
                            ( ( X4 @ X5 )
                           => ( ~ ( X2 @ X5 )
                             => ( X5 = X3 ) ) ) )
                 => ( X1 @ X4 ) ) )
       => ( X1 @ cB ) ) ) ).

thf(h1,negated_conjecture,
    ~ ( ~ ( sP4
         => ~ sP17 )
     => ! [X1: ( a > $o ) > $o] :
          ( ~ ( ! [X2: a > $o] :
                  ( ! [X3: a] :
                      ~ ( X2 @ X3 )
                 => ( X1 @ X2 ) )
             => ~ ! [X2: a > $o,X3: a,X4: a > $o] :
                    ( ~ ( ( X1 @ X2 )
                       => ~ ! [X5: a] :
                              ( ( X4 @ X5 )
                             => ( ~ ( X2 @ X5 )
                               => ( X5 = X3 ) ) ) )
                   => ( X1 @ X4 ) ) )
         => ( X1 @ cB ) ) ),
    inference(assume_negation,[status(cth)],[cTHM531E_pme]) ).

thf(h2,assumption,
    ~ ( sP4
     => ~ sP17 ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ! [X1: ( a > $o ) > $o] :
        ( ~ ( ! [X2: a > $o] :
                ( ! [X3: a] :
                    ~ ( X2 @ X3 )
               => ( X1 @ X2 ) )
           => ~ ! [X2: a > $o,X3: a,X4: a > $o] :
                  ( ~ ( ( X1 @ X2 )
                     => ~ ! [X5: a] :
                            ( ( X4 @ X5 )
                           => ( ~ ( X2 @ X5 )
                             => ( X5 = X3 ) ) ) )
                 => ( X1 @ X4 ) ) )
       => ( X1 @ cB ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP4,
    introduced(assumption,[]) ).

thf(h5,assumption,
    sP17,
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ ( ~ sP2
     => sP13 ),
    introduced(assumption,[]) ).

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

thf(h8,assumption,
    ~ sP13,
    introduced(assumption,[]) ).

thf(h9,assumption,
    sP12,
    introduced(assumption,[]) ).

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

thf(1,plain,
    ( ~ sP8
    | ~ sP5
    | sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP17
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP16
    | ~ sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( sP7
    | ~ sP16 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( sP7
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( sP18
    | ~ sP7 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__26]) ).

thf(7,plain,
    ( ~ sP3
    | ~ sP15
    | ~ sP18 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP11
    | sP3
    | sP13 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP14
    | sP11 ),
    inference(all_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP6
    | sP14 ),
    inference(all_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP1
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP2
    | ~ sP12
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP9
    | sP2
    | sP15 ),
    inference(prop_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP4
    | sP9 ),
    inference(all_rule,[status(thm)],]) ).

thf(15,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h9,h10,h7,h8,h6,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,h4,h5,h9,h10,h8]) ).

thf(16,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h7,h8,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h9,h10])],[h7,15,h9,h10]) ).

thf(17,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,16,h7,h8]) ).

thf(18,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__0)],[h3,17,h6]) ).

thf(19,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,18,h4,h5]) ).

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

thf(21,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[20,h0]) ).

thf(0,theorem,
    ( ~ ( sP4
       => ~ sP17 )
   => ! [X1: ( a > $o ) > $o] :
        ( ~ ( ! [X2: a > $o] :
                ( ! [X3: a] :
                    ~ ( X2 @ X3 )
               => ( X1 @ X2 ) )
           => ~ ! [X2: a > $o,X3: a,X4: a > $o] :
                  ( ~ ( ( X1 @ X2 )
                     => ~ ! [X5: a] :
                            ( ( X4 @ X5 )
                           => ( ~ ( X2 @ X5 )
                             => ( X5 = X3 ) ) ) )
                 => ( X1 @ X4 ) ) )
       => ( X1 @ cB ) ) ),
    inference(contra,[status(thm),contra(discharge,[h1])],[20,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU861^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n010.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  : 300
% 0.13/0.34  % DateTime : Wed Aug 23 18:44:21 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 1.30/1.50  % SZS status Theorem
% 1.30/1.50  % Mode: cade22grackle2xfee4
% 1.30/1.50  % Steps: 35631
% 1.30/1.50  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------