TSTP Solution File: LCL738^5 by Lash---1.13

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : LCL738^5 : 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 : n006.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 08:04:47 EDT 2023

% Result   : Theorem 20.17s 20.42s
% Output   : Proof 20.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   35
% Syntax   : Number of formulae    :   48 (  18 unt;   7 typ;   2 def)
%            Number of atoms       :   75 (   2 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  274 (  86   ~;  10   |;   0   &; 138   @)
%                                         (   8 <=>;  32  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   6 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   87 (  87   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  15 usr;  10 con; 0-3 aty)
%            Number of variables   :   75 (   2   ^;  67   !;   0   ?;  75   :)
%                                         (   0  !>;   0  ?*;   0  @-;   6  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_b,type,
    b: $tType ).

thf(ty_eigen__18,type,
    eigen__18: b > $o ).

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

thf(ty_eigen__20,type,
    eigen__20: b > $o ).

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

thf(ty_eigen__28,type,
    eigen__28: b > $o ).

thf(ty_eigen__2,type,
    eigen__2: ( b > $o ) > b ).

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

thf(eigendef_eigen__18,definition,
    ( eigen__18
    = ( eps__0
      @ ^ [X1: b > $o] :
          ~ ( ~ ! [X2: b] :
                  ~ ( X1 @ X2 )
           => ( X1
              @ @+[X2: b] : ( X1 @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__18])]) ).

thf(eigendef_eigen__28,definition,
    ( eigen__28
    = ( eps__0
      @ ^ [X1: b > $o] :
          ~ ( ~ ! [X2: b] :
                  ~ ( X1 @ X2 )
           => ( X1
              @ @+[X2: b] : ( X1 @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__28])]) ).

thf(sP1,plain,
    ( sP1
  <=> ( ~ ! [X1: b] :
            ~ ( eigen__18 @ X1 )
     => ( eigen__18
        @ @+[X1: b] : ( eigen__18 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: b] :
        ~ ( eigen__28 @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: b] :
        ~ ( eigen__18 @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( eigen__28
      @ @+[X1: b] : ( eigen__28 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: b > $o] :
        ( ~ ! [X2: b] :
              ~ ( X1 @ X2 )
       => ( X1
          @ @+[X2: b] : ( X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( eigen__18
      @ @+[X1: b] : ( eigen__18 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: ( b > $o ) > b] :
        ~ ! [X2: b > $o] :
            ( ~ ! [X3: b] :
                  ~ ( X2 @ X3 )
           => ( X2 @ ( X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ~ sP2
     => sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(cX5310_SUB,conjecture,
    ( ~ ! [X1: ( b > $o ) > b > b > $o,X2: ( b > $o ) > b > b > $o] :
          ~ ( ! [X3: b > $o] :
                ~ ! [X4: b] :
                    ~ ! [X5: b] :
                        ( ~ ( X2 @ X3 @ X4 @ X5 )
                       => ( X1 @ X3 @ X4 @ X5 ) )
           => ~ ! [X3: ( b > $o ) > b] :
                  ~ ! [X4: b > $o,X5: b] :
                      ( ~ ( X2 @ X4 @ ( X3 @ X4 ) @ X5 )
                     => ( X1 @ X4 @ ( X3 @ X4 ) @ X5 ) ) )
   => ~ sP7 ) ).

thf(h1,negated_conjecture,
    ~ ( ~ ! [X1: ( b > $o ) > b > b > $o,X2: ( b > $o ) > b > b > $o] :
            ~ ( ! [X3: b > $o] :
                  ~ ! [X4: b] :
                      ~ ! [X5: b] :
                          ( ~ ( X2 @ X3 @ X4 @ X5 )
                         => ( X1 @ X3 @ X4 @ X5 ) )
             => ~ ! [X3: ( b > $o ) > b] :
                    ~ ! [X4: b > $o,X5: b] :
                        ( ~ ( X2 @ X4 @ ( X3 @ X4 ) @ X5 )
                       => ( X1 @ X4 @ ( X3 @ X4 ) @ X5 ) ) )
     => ~ sP7 ),
    inference(assume_negation,[status(cth)],[cX5310_SUB]) ).

thf(h2,assumption,
    ~ ! [X1: ( b > $o ) > b > b > $o,X2: ( b > $o ) > b > b > $o] :
        ~ ( ! [X3: b > $o] :
              ~ ! [X4: b] :
                  ~ ! [X5: b] :
                      ( ~ ( X2 @ X3 @ X4 @ X5 )
                     => ( X1 @ X3 @ X4 @ X5 ) )
         => ~ ! [X3: ( b > $o ) > b] :
                ~ ! [X4: b > $o,X5: b] :
                    ( ~ ( X2 @ X4 @ ( X3 @ X4 ) @ X5 )
                   => ( X1 @ X4 @ ( X3 @ X4 ) @ X5 ) ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    sP7,
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ! [X1: ( b > $o ) > b > b > $o] :
        ~ ( ! [X2: b > $o] :
              ~ ! [X3: b] :
                  ~ ! [X4: b] :
                      ( ~ ( X1 @ X2 @ X3 @ X4 )
                     => ( eigen__0 @ X2 @ X3 @ X4 ) )
         => ~ ! [X2: ( b > $o ) > b] :
                ~ ! [X3: b > $o,X4: b] :
                    ( ~ ( X1 @ X3 @ ( X2 @ X3 ) @ X4 )
                   => ( eigen__0 @ X3 @ ( X2 @ X3 ) @ X4 ) ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    ( ! [X1: b > $o] :
        ~ ! [X2: b] :
            ~ ! [X3: b] :
                ( ~ ( eigen__1 @ X1 @ X2 @ X3 )
               => ( eigen__0 @ X1 @ X2 @ X3 ) )
   => ~ ! [X1: ( b > $o ) > b] :
          ~ ! [X2: b > $o,X3: b] :
              ( ~ ( eigen__1 @ X2 @ ( X1 @ X2 ) @ X3 )
             => ( eigen__0 @ X2 @ ( X1 @ X2 ) @ X3 ) ) ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ ! [X1: b > $o] :
        ~ ! [X2: b] :
            ~ ! [X3: b] :
                ( ~ ( eigen__1 @ X1 @ X2 @ X3 )
               => ( eigen__0 @ X1 @ X2 @ X3 ) ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    ~ ! [X1: ( b > $o ) > b] :
        ~ ! [X2: b > $o,X3: b] :
            ( ~ ( eigen__1 @ X2 @ ( X1 @ X2 ) @ X3 )
           => ( eigen__0 @ X2 @ ( X1 @ X2 ) @ X3 ) ),
    introduced(assumption,[]) ).

thf(h8,assumption,
    ! [X1: b] :
      ~ ! [X2: b] :
          ( ~ ( eigen__1 @ eigen__20 @ X1 @ X2 )
         => ( eigen__0 @ eigen__20 @ X1 @ X2 ) ),
    introduced(assumption,[]) ).

thf(1,plain,
    ( sP4
    | sP2 ),
    inference(choice_rule,[status(thm)],]) ).

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

thf(3,plain,
    ( sP8
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( sP5
    | ~ sP8 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__28]) ).

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

thf(6,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h8,h6,h5,h4,h2,h3,h1,h0])],[1,2,3,4,5,h3]) ).

thf(7,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h6,h5,h4,h2,h3,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__20)],[h6,6,h8]) ).

thf(h9,assumption,
    ! [X1: b > $o,X2: b] :
      ( ~ ( eigen__1 @ X1 @ ( eigen__2 @ X1 ) @ X2 )
     => ( eigen__0 @ X1 @ ( eigen__2 @ X1 ) @ X2 ) ),
    introduced(assumption,[]) ).

thf(8,plain,
    ( sP6
    | sP3 ),
    inference(choice_rule,[status(thm)],]) ).

thf(9,plain,
    ( sP1
    | ~ sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( sP1
    | ~ sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( sP5
    | ~ sP1 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__18]) ).

thf(12,plain,
    ( ~ sP7
    | ~ sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(13,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h9,h7,h5,h4,h2,h3,h1,h0])],[8,9,10,11,12,h3]) ).

thf(14,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h7,h5,h4,h2,h3,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__2)],[h7,13,h9]) ).

thf(15,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h5,h4,h2,h3,h1,h0]),tab_imp(discharge,[h6]),tab_imp(discharge,[h7])],[h5,7,14,h6,h7]) ).

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

thf(17,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__0)],[h2,16,h4]) ).

thf(18,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,17,h2,h3]) ).

thf(19,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[18,h0]) ).

thf(0,theorem,
    ( ~ ! [X1: ( b > $o ) > b > b > $o,X2: ( b > $o ) > b > b > $o] :
          ~ ( ! [X3: b > $o] :
                ~ ! [X4: b] :
                    ~ ! [X5: b] :
                        ( ~ ( X2 @ X3 @ X4 @ X5 )
                       => ( X1 @ X3 @ X4 @ X5 ) )
           => ~ ! [X3: ( b > $o ) > b] :
                  ~ ! [X4: b > $o,X5: b] :
                      ( ~ ( X2 @ X4 @ ( X3 @ X4 ) @ X5 )
                     => ( X1 @ X4 @ ( X3 @ X4 ) @ X5 ) ) )
   => ~ sP7 ),
    inference(contra,[status(thm),contra(discharge,[h1])],[18,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL738^5 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n006.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 : Thu Aug 24 22:37:22 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 20.17/20.42  % SZS status Theorem
% 20.17/20.42  % Mode: cade22grackle2x798d
% 20.17/20.42  % Steps: 1001
% 20.17/20.42  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------