%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEV179^5 : TPTP v8.1.0. Bugfixed v5.2.0.
% 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 18:05:14 EDT 2022

% Result   : Theorem 1.99s 2.17s
% Output   : Proof 1.99s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   17 (   9 unt;   1 typ;   2 def)
%            Number of atoms       :   36 (  15 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :  104 (  39   ~;   4   |;   0   &;  44   @)
%                                         (   4 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   24 (  24   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   7 con; 0-2 aty)
%            Number of variables   :   24 (  10   ^  14   !;   0   ?;  24   :)

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

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

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

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

thf(sP2,plain,
    ( sP2
  <=> ( sP1
     => ( ( eigen__0
          @ ^ [X1: $i] :
              ~ ! [X2: $i > $o] :
                  ( ~ ( X2 @ ( eigen__0 @ X2 ) )
                 => ( X1
                   != ( eigen__0 @ X2 ) ) ) )
       != ( eigen__0
          @ ^ [X1: $i] :
              ~ ! [X2: $i > $o] :
                  ( ~ ( X2 @ ( eigen__0 @ X2 ) )
                 => ( X1
                   != ( eigen__0 @ X2 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

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

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

thf(def_cD_FOR_X5309,definition,
    ( cD_FOR_X5309
    = ( ^ [X1: ( $i > $o ) > $i,X2: $i] :
          ~ ! [X3: $i > $o] :
              ( ~ ( X3 @ ( X1 @ X3 ) )
             => ( X2
               != ( X1 @ X3 ) ) ) ) ) ).

thf(cTHM144C_pme,conjecture,
    sP3 ).

thf(h1,negated_conjecture,
    ~ sP3,
    inference(assume_negation,[status(cth)],[cTHM144C_pme]) ).

thf(1,plain,
    sP4,
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP2
    | ~ sP1
    | ~ sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP1
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( sP3
    | sP1 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).

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

thf(6,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[5,h0]) ).

thf(0,theorem,
    sP3,
    inference(contra,[status(thm),contra(discharge,[h1])],[5,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEV179^5 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.07/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n009.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Tue Jun 28 07:01:22 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 1.99/2.17  % SZS status Theorem
% 1.99/2.17  % Mode: mode506
% 1.99/2.17  % Inferences: 5
% 1.99/2.17  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------