TSTP Solution File: SEU974^5 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEU974^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n024.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  : 600s
% DateTime : Tue Jul 19 14:11:06 EDT 2022

% Result   : Theorem 1.94s 2.21s
% Output   : Proof 1.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   39
% Syntax   : Number of formulae    :   47 (  11 unt;   8 typ;   3 def)
%            Number of atoms       :  121 (  46 equ;   0 cnn)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :  531 ( 120   ~;  16   |;   0   &; 286   @)
%                                         (  14 <=>;  95  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   6 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   22 (  22   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   25 (  23 usr;  20 con; 0-2 aty)
%            Number of variables   :   59 (   3   ^  56   !;   0   ?;  59   :)

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

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

thf(ty_cP,type,
    cP: a > a > a ).

thf(ty_cL,type,
    cL: a > a ).

thf(ty_eigen__1,type,
    eigen__1: a ).

thf(ty_eigen__0,type,
    eigen__0: a ).

thf(ty_cR,type,
    cR: a > a ).

thf(ty_cZ,type,
    cZ: a ).

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

thf(eigendef_eigen__1,definition,
    ( eigen__1
    = ( eps__0
      @ ^ [X1: a] :
          ~ ( ~ ! [X2: a > $o] :
                  ( ( X2 @ ( cP @ eigen__0 @ X1 ) )
                 => ~ ! [X3: a,X4: a] :
                        ( ( X2 @ ( cP @ X3 @ X4 ) )
                       => ~ ( ~ ( ( ( X4 = cZ )
                                 => ( X3 = cZ ) )
                               => ~ ( X2 @ ( cP @ ( cL @ X3 ) @ ( cL @ X4 ) ) ) )
                           => ~ ( X2 @ ( cP @ ( cR @ X3 ) @ ( cR @ X4 ) ) ) ) ) )
           => ~ ! [X2: a > $o] :
                  ( ( X2 @ ( cP @ ( cR @ eigen__0 ) @ ( cR @ X1 ) ) )
                 => ~ ! [X3: a,X4: a] :
                        ( ( X2 @ ( cP @ X3 @ X4 ) )
                       => ~ ( ~ ( ( ( X4 = cZ )
                                 => ( X3 = cZ ) )
                               => ~ ( X2 @ ( cP @ ( cL @ X3 ) @ ( cL @ X4 ) ) ) )
                           => ~ ( X2 @ ( cP @ ( cR @ X3 ) @ ( cR @ X4 ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__1])]) ).

thf(eigendef_eigen__0,definition,
    ( eigen__0
    = ( eps__0
      @ ^ [X1: a] :
          ~ ! [X2: a] :
              ( ~ ! [X3: a > $o] :
                    ( ( X3 @ ( cP @ X1 @ X2 ) )
                   => ~ ! [X4: a,X5: a] :
                          ( ( X3 @ ( cP @ X4 @ X5 ) )
                         => ~ ( ~ ( ( ( X5 = cZ )
                                   => ( X4 = cZ ) )
                                 => ~ ( X3 @ ( cP @ ( cL @ X4 ) @ ( cL @ X5 ) ) ) )
                             => ~ ( X3 @ ( cP @ ( cR @ X4 ) @ ( cR @ X5 ) ) ) ) ) )
             => ~ ! [X3: a > $o] :
                    ( ( X3 @ ( cP @ ( cR @ X1 ) @ ( cR @ X2 ) ) )
                   => ~ ! [X4: a,X5: a] :
                          ( ( X3 @ ( cP @ X4 @ X5 ) )
                         => ~ ( ~ ( ( ( X5 = cZ )
                                   => ( X4 = cZ ) )
                                 => ~ ( X3 @ ( cP @ ( cL @ X4 ) @ ( cL @ X5 ) ) ) )
                             => ~ ( X3 @ ( cP @ ( cR @ X4 ) @ ( cR @ X5 ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__0])]) ).

thf(h1,assumption,
    ! [X1: ( a > $o ) > $o,X2: a > $o] :
      ( ( X1 @ X2 )
     => ( X1 @ ( eps__1 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(eigendef_eigen__2,definition,
    ( eigen__2
    = ( eps__1
      @ ^ [X1: a > $o] :
          ~ ( ( X1 @ ( cP @ eigen__0 @ eigen__1 ) )
           => ~ ! [X2: a,X3: a] :
                  ( ( X1 @ ( cP @ X2 @ X3 ) )
                 => ~ ( ~ ( ( ( X3 = cZ )
                           => ( X2 = cZ ) )
                         => ~ ( X1 @ ( cP @ ( cL @ X2 ) @ ( cL @ X3 ) ) ) )
                     => ~ ( X1 @ ( cP @ ( cR @ X2 ) @ ( cR @ X3 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__2])]) ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: a > $o] :
        ( ( X1 @ ( cP @ ( cR @ eigen__0 ) @ ( cR @ eigen__1 ) ) )
       => ~ ! [X2: a,X3: a] :
              ( ( X1 @ ( cP @ X2 @ X3 ) )
             => ~ ( ~ ( ( ( X3 = cZ )
                       => ( X2 = cZ ) )
                     => ~ ( X1 @ ( cP @ ( cL @ X2 ) @ ( cL @ X3 ) ) ) )
                 => ~ ( X1 @ ( cP @ ( cR @ X2 ) @ ( cR @ X3 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: a,X2: a] :
        ( ( eigen__2 @ ( cP @ X1 @ X2 ) )
       => ~ ( ~ ( ( ( X2 = cZ )
                 => ( X1 = cZ ) )
               => ~ ( eigen__2 @ ( cP @ ( cL @ X1 ) @ ( cL @ X2 ) ) ) )
           => ~ ( eigen__2 @ ( cP @ ( cR @ X1 ) @ ( cR @ X2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ~ ! [X1: a > $o] :
            ( ( X1 @ ( cP @ eigen__0 @ eigen__1 ) )
           => ~ ! [X2: a,X3: a] :
                  ( ( X1 @ ( cP @ X2 @ X3 ) )
                 => ~ ( ~ ( ( ( X3 = cZ )
                           => ( X2 = cZ ) )
                         => ~ ( X1 @ ( cP @ ( cL @ X2 ) @ ( cL @ X3 ) ) ) )
                     => ~ ( X1 @ ( cP @ ( cR @ X2 ) @ ( cR @ X3 ) ) ) ) ) )
     => ~ sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: a > $o] :
        ( ( X1 @ ( cP @ eigen__0 @ eigen__1 ) )
       => ~ ! [X2: a,X3: a] :
              ( ( X1 @ ( cP @ X2 @ X3 ) )
             => ~ ( ~ ( ( ( X3 = cZ )
                       => ( X2 = cZ ) )
                     => ~ ( X1 @ ( cP @ ( cL @ X2 ) @ ( cL @ X3 ) ) ) )
                 => ~ ( X1 @ ( cP @ ( cR @ X2 ) @ ( cR @ X3 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( eigen__2 @ ( cP @ ( cR @ eigen__0 ) @ ( cR @ eigen__1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ( eigen__2 @ ( cP @ eigen__0 @ eigen__1 ) )
     => ~ ( ~ ( ( ( eigen__1 = cZ )
               => ( eigen__0 = cZ ) )
             => ~ ( eigen__2 @ ( cP @ ( cL @ eigen__0 ) @ ( cL @ eigen__1 ) ) ) )
         => ~ sP5 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( sP5
     => ~ sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( eigen__2 @ ( cP @ eigen__0 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ! [X1: a,X2: a] :
        ( ~ ! [X3: a > $o] :
              ( ( X3 @ ( cP @ X1 @ X2 ) )
             => ~ ! [X4: a,X5: a] :
                    ( ( X3 @ ( cP @ X4 @ X5 ) )
                   => ~ ( ~ ( ( ( X5 = cZ )
                             => ( X4 = cZ ) )
                           => ~ ( X3 @ ( cP @ ( cL @ X4 ) @ ( cL @ X5 ) ) ) )
                       => ~ ( X3 @ ( cP @ ( cR @ X4 ) @ ( cR @ X5 ) ) ) ) ) )
       => ~ ! [X3: a > $o] :
              ( ( X3 @ ( cP @ ( cR @ X1 ) @ ( cR @ X2 ) ) )
             => ~ ! [X4: a,X5: a] :
                    ( ( X3 @ ( cP @ X4 @ X5 ) )
                   => ~ ( ~ ( ( ( X5 = cZ )
                             => ( X4 = cZ ) )
                           => ~ ( X3 @ ( cP @ ( cL @ X4 ) @ ( cL @ X5 ) ) ) )
                       => ~ ( X3 @ ( cP @ ( cR @ X4 ) @ ( cR @ X5 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
                            = cZ )
                         => ( ( cR @ cZ )
                           != cZ ) )
                     => ~ ! [X1: a,X2: a] :
                            ( ( cL @ ( cP @ X1 @ X2 ) )
                            = X1 ) )
                 => ~ ! [X1: a,X2: a] :
                        ( ( cR @ ( cP @ X1 @ X2 ) )
                        = X2 ) )
             => ~ ! [X1: a] :
                    ( ( ( X1 != cZ ) )
                    = ( X1
                      = ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) )
         => ~ ! [X1: a > $o] :
                ( ! [X2: a,X3: a] :
                    ( ( X1 @ ( cP @ X2 @ X3 ) )
                   => ~ ( ~ ( ( ( X2 = cZ )
                              = ( X3 = cZ ) )
                           => ~ ( X1 @ ( cP @ ( cL @ X2 ) @ ( cL @ X3 ) ) ) )
                       => ~ ( X1 @ ( cP @ ( cR @ X2 ) @ ( cR @ X3 ) ) ) ) )
               => ! [X2: a,X3: a] :
                    ( ( X1 @ ( cP @ X2 @ X3 ) )
                   => ( X2 = X3 ) ) ) )
     => sP9 ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( sP8
     => ~ sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ! [X1: a] :
        ( ( eigen__2 @ ( cP @ eigen__0 @ X1 ) )
       => ~ ( ~ ( ( ( X1 = cZ )
                 => ( eigen__0 = cZ ) )
               => ~ ( eigen__2 @ ( cP @ ( cL @ eigen__0 ) @ ( cL @ X1 ) ) ) )
           => ~ ( eigen__2 @ ( cP @ ( cR @ eigen__0 ) @ ( cR @ X1 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( ~ ( ( ( eigen__1 = cZ )
           => ( eigen__0 = cZ ) )
         => ~ ( eigen__2 @ ( cP @ ( cL @ eigen__0 ) @ ( cL @ eigen__1 ) ) ) )
     => ~ sP5 ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ! [X1: a] :
        ( ~ ! [X2: a > $o] :
              ( ( X2 @ ( cP @ eigen__0 @ X1 ) )
             => ~ ! [X3: a,X4: a] :
                    ( ( X2 @ ( cP @ X3 @ X4 ) )
                   => ~ ( ~ ( ( ( X4 = cZ )
                             => ( X3 = cZ ) )
                           => ~ ( X2 @ ( cP @ ( cL @ X3 ) @ ( cL @ X4 ) ) ) )
                       => ~ ( X2 @ ( cP @ ( cR @ X3 ) @ ( cR @ X4 ) ) ) ) ) )
       => ~ ! [X2: a > $o] :
              ( ( X2 @ ( cP @ ( cR @ eigen__0 ) @ ( cR @ X1 ) ) )
             => ~ ! [X3: a,X4: a] :
                    ( ( X2 @ ( cP @ X3 @ X4 ) )
                   => ~ ( ~ ( ( ( X4 = cZ )
                             => ( X3 = cZ ) )
                           => ~ ( X2 @ ( cP @ ( cL @ X3 ) @ ( cL @ X4 ) ) ) )
                       => ~ ( X2 @ ( cP @ ( cR @ X3 ) @ ( cR @ X4 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(cPU_LEM2C_pme,conjecture,
    sP10 ).

thf(h2,negated_conjecture,
    ~ sP10,
    inference(assume_negation,[status(cth)],[cPU_LEM2C_pme]) ).

thf(1,plain,
    ( sP13
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP6
    | ~ sP8
    | ~ sP13 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP7
    | ~ sP5
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP12
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP1
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP2
    | sP12 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( sP11
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP11
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( sP4
    | ~ sP11 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2]) ).

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

thf(11,plain,
    ( sP3
    | ~ sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    ( sP14
    | ~ sP3 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).

thf(13,plain,
    ( sP9
    | ~ sP14 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).

thf(14,plain,
    ( sP10
    | ~ sP9 ),
    inference(prop_rule,[status(thm)],]) ).

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

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

thf(17,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[16,h0]) ).

thf(0,theorem,
    sP10,
    inference(contra,[status(thm),contra(discharge,[h2])],[15,h2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SEU974^5 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34  % Computer : n024.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sun Jun 19 02:51:47 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 1.94/2.21  % SZS status Theorem
% 1.94/2.21  % Mode: mode506
% 1.94/2.21  % Inferences: 19477
% 1.94/2.21  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------