TSTP Solution File: SEV055^5 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEV055^5 : 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 : n009.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 18:04:39 EDT 2022

% Result   : Theorem 46.30s 45.96s
% Output   : Proof 46.30s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   40
% Syntax   : Number of formulae    :   51 (  18 unt;   5 typ;   4 def)
%            Number of atoms       :  136 (   4 equ;   0 cnn)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  388 (  70   ~;  15   |;   0   &; 213   @)
%                                         (  15 <=>;  75  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   43 (  43   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   25 (  23 usr;  21 con; 0-2 aty)
%            Number of variables   :  101 (  14   ^  87   !;   0   ?; 101   :)

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

thf(ty_eigen__12,type,
    eigen__12: a ).

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

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

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

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

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

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

thf(eigendef_eigen__0,definition,
    ( eigen__0
    = ( eps__1
      @ ^ [X1: a > a > $o] :
          ~ ! [X2: ( a > $o ) > a] :
              ( ~ ( ! [X3: a,X4: a,X5: a] :
                      ( ~ ( ( X1 @ X3 @ X4 )
                         => ~ ( X1 @ X4 @ X5 ) )
                     => ( X1 @ X3 @ X5 ) )
                 => ~ ! [X3: a > $o] :
                        ~ ( ! [X4: a] :
                              ( ( X3 @ X4 )
                             => ( X1 @ X4 @ ( X2 @ X3 ) ) )
                         => ~ ! [X4: a] :
                                ( ! [X5: a] :
                                    ( ( X3 @ X5 )
                                   => ( X1 @ X5 @ X4 ) )
                               => ( X1 @ ( X2 @ X3 ) @ X4 ) ) ) )
             => ! [X3: a > a] :
                  ( ! [X4: a,X5: a] :
                      ( ( X1 @ X4 @ X5 )
                     => ( X1 @ ( X3 @ X4 ) @ ( X3 @ X5 ) ) )
                 => ~ ! [X4: a] :
                        ~ ( X1 @ X4 @ ( X3 @ X4 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__0])]) ).

thf(h2,assumption,
    ! [X1: a > $o,X2: a] :
      ( ( X1 @ X2 )
     => ( X1 @ ( eps__2 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(eigendef_eigen__12,definition,
    ( eigen__12
    = ( eps__2
      @ ^ [X1: a] :
          ~ ( $false
           => ( eigen__0 @ X1
              @ ( eigen__2
                @ ( eigen__1
                  @ ^ [X2: a] : $false ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__12])]) ).

thf(h3,assumption,
    ! [X1: ( a > a ) > $o,X2: a > a] :
      ( ( X1 @ X2 )
     => ( X1 @ ( eps__3 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(eigendef_eigen__2,definition,
    ( eigen__2
    = ( eps__3
      @ ^ [X1: a > a] :
          ~ ( ! [X2: a,X3: a] :
                ( ( eigen__0 @ X2 @ X3 )
               => ( eigen__0 @ ( X1 @ X2 ) @ ( X1 @ X3 ) ) )
           => ~ ! [X2: a] :
                  ~ ( eigen__0 @ X2 @ ( X1 @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__2])]) ).

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

thf(sP2,plain,
    ( sP2
  <=> ! [X1: a > a] :
        ( ! [X2: a,X3: a] :
            ( ( eigen__0 @ X2 @ X3 )
           => ( eigen__0 @ ( X1 @ X2 ) @ ( X1 @ X3 ) ) )
       => ~ ! [X2: a] :
              ~ ( eigen__0 @ X2 @ ( X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: a] :
        ( $false
       => ( eigen__0 @ X1
          @ ( eigen__2
            @ ( eigen__1
              @ ^ [X2: a] : $false ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ! [X1: a,X2: a] :
          ( ( eigen__0 @ X1 @ X2 )
         => ( eigen__0 @ ( eigen__2 @ X1 ) @ ( eigen__2 @ X2 ) ) )
     => ~ ! [X1: a] :
            ~ ( eigen__0 @ X1 @ ( eigen__2 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( sP3
     => ( eigen__0
        @ ( eigen__1
          @ ^ [X1: a] : $false )
        @ ( eigen__2
          @ ( eigen__1
            @ ^ [X1: a] : $false ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( eigen__0
      @ ( eigen__1
        @ ^ [X1: a] : sP6 )
      @ ( eigen__2
        @ ( eigen__1
          @ ^ [X1: a] : sP6 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ! [X1: a] :
          ( sP6
         => ( eigen__0 @ X1
            @ ( eigen__1
              @ ^ [X2: a] : sP6 ) ) )
     => ~ ! [X1: a] :
            ( ! [X2: a] :
                ( sP6
               => ( eigen__0 @ X2 @ X1 ) )
           => ( eigen__0
              @ ( eigen__1
                @ ^ [X2: a] : sP6 )
              @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( sP6
     => ( eigen__0 @ eigen__12
        @ ( eigen__2
          @ ( eigen__1
            @ ^ [X1: a] : sP6 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ! [X1: a] :
        ( ! [X2: a] :
            ( sP6
           => ( eigen__0 @ X2 @ X1 ) )
       => ( eigen__0
          @ ( eigen__1
            @ ^ [X2: a] : sP6 )
          @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( ~ ( ! [X1: a,X2: a,X3: a] :
              ( ~ ( ( eigen__0 @ X1 @ X2 )
                 => ~ ( eigen__0 @ X2 @ X3 ) )
             => ( eigen__0 @ X1 @ X3 ) )
         => ~ ! [X1: a > $o] :
                ~ ( ! [X2: a] :
                      ( ( X1 @ X2 )
                     => ( eigen__0 @ X2 @ ( eigen__1 @ X1 ) ) )
                 => ~ ! [X2: a] :
                        ( ! [X3: a] :
                            ( ( X1 @ X3 )
                           => ( eigen__0 @ X3 @ X2 ) )
                       => ( eigen__0 @ ( eigen__1 @ X1 ) @ X2 ) ) ) )
     => sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ! [X1: a > a > $o,X2: ( a > $o ) > a] :
        ( ~ ( ! [X3: a,X4: a,X5: a] :
                ( ~ ( ( X1 @ X3 @ X4 )
                   => ~ ( X1 @ X4 @ X5 ) )
               => ( X1 @ X3 @ X5 ) )
           => ~ ! [X3: a > $o] :
                  ~ ( ! [X4: a] :
                        ( ( X3 @ X4 )
                       => ( X1 @ X4 @ ( X2 @ X3 ) ) )
                   => ~ ! [X4: a] :
                          ( ! [X5: a] :
                              ( ( X3 @ X5 )
                             => ( X1 @ X5 @ X4 ) )
                         => ( X1 @ ( X2 @ X3 ) @ X4 ) ) ) )
       => ! [X3: a > a] :
            ( ! [X4: a,X5: a] :
                ( ( X1 @ X4 @ X5 )
               => ( X1 @ ( X3 @ X4 ) @ ( X3 @ X5 ) ) )
           => ~ ! [X4: a] :
                  ~ ( X1 @ X4 @ ( X3 @ X4 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ! [X1: a] :
        ~ ( eigen__0 @ X1 @ ( eigen__2 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ! [X1: a > $o] :
        ~ ( ! [X2: a] :
              ( ( X1 @ X2 )
             => ( eigen__0 @ X2 @ ( eigen__1 @ X1 ) ) )
         => ~ ! [X2: a] :
                ( ! [X3: a] :
                    ( ( X1 @ X3 )
                   => ( eigen__0 @ X3 @ X2 ) )
               => ( eigen__0 @ ( eigen__1 @ X1 ) @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( ! [X1: a,X2: a,X3: a] :
          ( ~ ( ( eigen__0 @ X1 @ X2 )
             => ~ ( eigen__0 @ X2 @ X3 ) )
         => ( eigen__0 @ X1 @ X3 ) )
     => ~ sP14 ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(cTHM402_pme,conjecture,
    sP12 ).

thf(h4,negated_conjecture,
    ~ sP12,
    inference(assume_negation,[status(cth)],[cTHM402_pme]) ).

thf(1,plain,
    ( sP9
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( sP3
    | ~ sP9 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__12]) ).

thf(3,plain,
    ( ~ sP5
    | ~ sP3
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP10
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP13
    | ~ sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( sP4
    | sP13 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ~ sP6,
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP8
    | sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP14
    | ~ sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(10,plain,
    ( sP15
    | sP14 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( sP2
    | ~ sP4 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h3])],[h3,eigendef_eigen__2]) ).

thf(12,plain,
    ( sP11
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(13,plain,
    ( sP11
    | ~ sP15 ),
    inference(prop_rule,[status(thm)],]) ).

thf(14,plain,
    ( sP1
    | ~ sP11 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).

thf(15,plain,
    ( sP12
    | ~ sP1 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).

thf(16,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,h4]) ).

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

thf(18,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h4,h1,h0]),eigenvar_choice(discharge,[h2])],[17,h2]) ).

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

thf(20,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h4]),eigenvar_choice(discharge,[h0])],[19,h0]) ).

thf(0,theorem,
    sP12,
    inference(contra,[status(thm),contra(discharge,[h4])],[16,h4]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEV055^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n009.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  : 600
% 0.12/0.33  % DateTime : Tue Jun 28 01:47:07 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 46.30/45.96  % SZS status Theorem
% 46.30/45.96  % Mode: mode456
% 46.30/45.96  % Inferences: 10913
% 46.30/45.96  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------