TSTP Solution File: SYO517^1 by Lash---1.13

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%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SYO517^1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n007.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 : Fri Sep  1 04:47:20 EDT 2023

% Result   : Theorem 20.14s 20.45s
% Output   : Proof 20.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   28 (  10 unt;   2 typ;   2 def)
%            Number of atoms       :   58 (   9 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   95 (  25   ~;   8   |;   0   &;  34   @)
%                                         (   8 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  12 usr;  12 con; 0-2 aty)
%            Number of variables   :   26 (   2   ^;  20   !;   0   ?;  26   :)
%                                         (   0  !>;   0  ?*;   0  @-;   4  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_eigen__8,type,
    eigen__8: $i ).

thf(ty_eigen__7,type,
    eigen__7: $i > $o ).

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

thf(eigendef_eigen__8,definition,
    ( eigen__8
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ( ( eigen__7 @ X1 )
           => ~ ! [X2: $i] :
                  ( ( eigen__7 @ X2 )
                 => ( X1 = X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__8])]) ).

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

thf(eigendef_eigen__7,definition,
    ( eigen__7
    = ( eps__1
      @ ^ [X1: $i > $o] :
          ~ ( ~ ! [X2: $i] :
                  ( ( X1 @ X2 )
                 => ~ ! [X3: $i] :
                        ( ( X1 @ X3 )
                       => ( X2 = X3 ) ) )
           => ( X1
              @ @+[X2: $i] : ( X1 @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__7])]) ).

thf(sP1,plain,
    ( sP1
  <=> ( ( eigen__7 @ eigen__8 )
     => ~ ! [X1: $i] :
            ( ( eigen__7 @ X1 )
           => ( eigen__8 = X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: $i] :
        ~ ( eigen__7 @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: ( $i > $o ) > $i] :
        ~ ! [X2: $i > $o] :
            ( ~ ! [X3: $i] :
                  ( ( X2 @ X3 )
                 => ~ ! [X4: $i] :
                        ( ( X2 @ X4 )
                       => ( X3 = X4 ) ) )
           => ( X2 @ ( X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

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

thf(sP5,plain,
    ( sP5
  <=> ( ~ ! [X1: $i] :
            ( ( eigen__7 @ X1 )
           => ~ ! [X2: $i] :
                  ( ( eigen__7 @ X2 )
                 => ( X1 = X2 ) ) )
     => ( eigen__7
        @ @+[X1: $i] : ( eigen__7 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( eigen__7 @ eigen__8 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: $i] :
        ( ( eigen__7 @ X1 )
       => ~ ! [X2: $i] :
              ( ( eigen__7 @ X2 )
             => ( X1 = X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( eigen__7
      @ @+[X1: $i] : ( eigen__7 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(descri,conjecture,
    ~ sP3 ).

thf(h2,negated_conjecture,
    sP3,
    inference(assume_negation,[status(cth)],[descri]) ).

thf(1,plain,
    ( ~ sP2
    | ~ sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( sP8
    | sP2 ),
    inference(choice_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP1
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( sP7
    | ~ sP1 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).

thf(5,plain,
    ( sP5
    | ~ sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( sP5
    | ~ sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( sP4
    | ~ sP5 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__7]) ).

thf(8,plain,
    ( ~ sP3
    | ~ sP4 ),
    inference(all_rule,[status(thm)],]) ).

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

thf(10,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[9,h1]) ).

thf(11,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[10,h0]) ).

thf(0,theorem,
    ~ sP3,
    inference(contra,[status(thm),contra(discharge,[h2])],[9,h2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SYO517^1 : TPTP v8.1.2. Released v4.1.0.
% 0.10/0.12  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.10/0.32  % Computer : n007.cluster.edu
% 0.10/0.32  % Model    : x86_64 x86_64
% 0.10/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32  % Memory   : 8042.1875MB
% 0.10/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit : 300
% 0.10/0.32  % WCLimit  : 300
% 0.10/0.32  % DateTime : Sat Aug 26 04:26:11 EDT 2023
% 0.10/0.32  % CPUTime  : 
% 20.14/20.45  % SZS status Theorem
% 20.14/20.45  % Mode: cade22grackle2x798d
% 20.14/20.45  % Steps: 1122
% 20.14/20.45  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------