TSTP Solution File: LCL727^5 by Satallax---3.5

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%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : LCL727^5 : 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 : n013.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 : Sun Jul 17 14:10:37 EDT 2022

% Result   : Theorem 33.23s 33.42s
% Output   : Proof 33.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   28
% Syntax   : Number of formulae    :   35 (  11 unt;   3 typ;   2 def)
%            Number of atoms       :   64 (   2 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :  111 (  32   ~;  12   |;   0   &;  39   @)
%                                         (  11 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   35 (  35   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  15 usr;  14 con; 0-2 aty)
%            Number of variables   :   29 (   2   ^  24   !;   0   ?;  29   :)
%                                         (   0  !>;   0  ?*;   0  @-;   3  @+)

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

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

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

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

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

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

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

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

thf(sP2,plain,
    ( sP2
  <=> ( eigen__1
      @ @+[X1: a] : ( eigen__1 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: a > $o] :
        ( ( eigen__0 @ X1 )
       => ~ ! [X2: a] :
              ~ ( X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

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

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

thf(sP6,plain,
    ( sP6
  <=> ! [X1: ( a > $o ) > $o] :
        ( ! [X2: a > $o] :
            ( ( X1 @ X2 )
           => ~ ! [X3: a] :
                  ~ ( X2 @ X3 ) )
       => ~ ! [X2: ( a > $o ) > a] :
              ~ ! [X3: a > $o] :
                  ( ( X1 @ X3 )
                 => ( X3 @ ( X2 @ X3 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( sP5
     => ~ ! [X1: a] :
            ~ ( eigen__1 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ! [X1: ( a > $o ) > a > $o] :
          ~ ! [X2: ( a > $o ) > a] :
              ~ ! [X3: a > $o] :
                  ( ~ ! [X4: a] :
                        ~ ( X1 @ X3 @ X4 )
                 => ( X1 @ X3 @ ( X2 @ X3 ) ) )
     => sP6 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ! [X1: a] :
        ~ ( eigen__1 @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( sP5
     => sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( sP3
     => ~ sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(cTHM533,conjecture,
    sP8 ).

thf(h2,negated_conjecture,
    ~ sP8,
    inference(assume_negation,[status(cth)],[cTHM533]) ).

thf(1,plain,
    ( sP2
    | sP9 ),
    inference(choice_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP7
    | ~ sP5
    | ~ sP9 ),
    inference(prop_rule,[status(thm)],]) ).

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

thf(4,plain,
    ( sP10
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( sP10
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( sP1
    | ~ sP10 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).

thf(7,plain,
    ( ~ sP4
    | ~ sP1 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP11
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( sP11
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( sP6
    | ~ sP11 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).

thf(11,plain,
    ( sP8
    | ~ sP6 ),
    inference(prop_rule,[status(thm)],]) ).

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

thf(13,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[12,h1]) ).

thf(14,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[13,h0]) ).

thf(0,theorem,
    sP8,
    inference(contra,[status(thm),contra(discharge,[h2])],[12,h2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL727^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n013.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 : Sun Jul  3 15:31:59 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 33.23/33.42  % SZS status Theorem
% 33.23/33.42  % Mode: mode448
% 33.23/33.42  % Inferences: 360
% 33.23/33.42  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------