TSTP Solution File: SYO300^5 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SYO300^5 : 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 : n026.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 : Thu Jul 21 19:31:20 EDT 2022

% Result   : Theorem 1.96s 2.19s
% Output   : Proof 1.96s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   20 (   8 unt;   1 typ;   1 def)
%            Number of atoms       :   41 (   1 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   82 (  13   ~;   6   |;   0   &;  51   @)
%                                         (   6 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   70 (  70   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   8 con; 0-2 aty)
%            Number of variables   :   43 (  25   ^  12   !;   0   ?;  43   :)
%                                         (   0  !>;   0  ?*;   0  @-;   6  @+)

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

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

thf(eigendef_eigen__0,definition,
    ( eigen__0
    = ( eps__0
      @ ^ [X1: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > $i ) > $o] :
          ~ ~ ! [X2: ( $i > $i ) > $i] :
                ~ ( ! [X3: ( $i > $i ) > $i] : ( X1 @ X3 @ X3 )
                 => ( X1
                    @ ^ [X3: $i > $i] :
                        ( X3
                        @ ( X2
                          @ ^ [X4: $i] : X4 ) )
                    @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__0])]) ).

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

thf(sP2,plain,
    ( sP2
  <=> ( ! [X1: ( $i > $i ) > $i] : ( eigen__0 @ X1 @ X1 )
     => ( eigen__0
        @ ^ [X1: $i > $i] :
            ( X1
            @ @+[X2: $i] :
                ( eigen__0
                @ ^ [X3: $i > $i] : X2
                @ ^ [X3: $i > $i] : X2 ) )
        @ ^ [X1: $i > $i] :
            ( X1
            @ @+[X2: $i] :
                ( eigen__0
                @ ^ [X3: $i > $i] : X2
                @ ^ [X3: $i > $i] : X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( eigen__0
      @ ^ [X1: $i > $i] :
          ( X1
          @ @+[X2: $i] :
              ( eigen__0
              @ ^ [X3: $i > $i] : X2
              @ ^ [X3: $i > $i] : X2 ) )
      @ ^ [X1: $i > $i] :
          ( X1
          @ @+[X2: $i] :
              ( eigen__0
              @ ^ [X3: $i > $i] : X2
              @ ^ [X3: $i > $i] : X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ! [X1: ( $i > $i ) > $i] : ( eigen__0 @ X1 @ X1 )
     => ( eigen__0
        @ ^ [X1: $i > $i] :
            ( X1
            @ @+[X2: $i] :
                ( eigen__0
                @ ^ [X3: $i > $i] : X2
                @ ^ [X3: $i > $i] : X2 ) )
        @ ^ [X1: $i > $i] :
          @+[X2: $i] :
            ( eigen__0
            @ ^ [X3: $i > $i] : X2
            @ ^ [X3: $i > $i] : X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > $i ) > $o] :
        ~ ! [X2: ( $i > $i ) > $i] :
            ~ ( ! [X3: ( $i > $i ) > $i] : ( X1 @ X3 @ X3 )
             => ( X1
                @ ^ [X3: $i > $i] :
                    ( X3
                    @ ( X2
                      @ ^ [X4: $i] : X4 ) )
                @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

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

thf(cUNIFTHM1,conjecture,
    sP5 ).

thf(h1,negated_conjecture,
    ~ sP5,
    inference(assume_negation,[status(cth)],[cUNIFTHM1]) ).

thf(1,plain,
    ( sP2
    | ~ sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP1
    | ~ sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP6
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( sP4
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP1
    | ~ sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( sP5
    | sP1 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).

thf(7,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,h1]) ).

thf(8,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[7,h0]) ).

thf(0,theorem,
    sP5,
    inference(contra,[status(thm),contra(discharge,[h1])],[7,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SYO300^5 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n026.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 : Fri Jul  8 23:17:10 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.96/2.19  % SZS status Theorem
% 1.96/2.19  % Mode: mode506
% 1.96/2.19  % Inferences: 19399
% 1.96/2.19  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------