%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SYO281^5 : 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 : n025.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 19:31:14 EDT 2022

% Result   : Theorem 0.13s 0.37s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   19 (   7 unt;   2 typ;   1 def)
%            Number of atoms       :   26 (   1 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   46 (  16   ~;   3   |;   0   &;  15   @)
%                                         (   4 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   7 con; 0-2 aty)
%            Number of variables   :   15 (   1   ^  14   !;   0   ?;  15   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
    eigen__2: $i ).

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

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

thf(eigendef_eigen__2,definition,
    ( eigen__2
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ( ( eigen__0 @ X1 )
           => ~ $false ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__2])]) ).

thf(sP1,plain,
    ( sP1
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( eigen__0 @ eigen__2 )
     => ~ sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

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

thf(sP4,plain,
    ( sP4
  <=> ! [X1: $i] :
        ( ( eigen__0 @ X1 )
       => ~ sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(cTRIV3,conjecture,
    ! [X1: $i > $o] :
      ~ ! [X2: $i > $o] :
          ~ ! [X3: $i] :
              ( ( X1 @ X3 )
             => ( X2 @ X3 ) ) ).

thf(h1,negated_conjecture,
    ~ ! [X1: $i > $o] :
        ~ ! [X2: $i > $o] :
            ~ ! [X3: $i] :
                ( ( X1 @ X3 )
               => ( X2 @ X3 ) ),
    inference(assume_negation,[status(cth)],[cTRIV3]) ).

thf(h2,assumption,
    sP3,
    introduced(assumption,[]) ).

thf(1,plain,
    ~ sP1,
    inference(prop_rule,[status(thm)],]) ).

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

thf(3,plain,
    ( sP4
    | ~ sP2 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).

thf(4,plain,
    ( ~ sP3
    | ~ sP4 ),
    inference(all_rule,[status(thm)],]) ).

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

thf(6,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,5,h2]) ).

thf(7,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[6,h0]) ).

thf(0,theorem,
    ! [X1: $i > $o] :
      ~ ! [X2: $i > $o] :
          ~ ! [X3: $i] :
              ( ( X1 @ X3 )
             => ( X2 @ X3 ) ),
    inference(contra,[status(thm),contra(discharge,[h1])],[6,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYO281^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n025.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 : Sat Jul  9 14:24:45 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.37  % SZS status Theorem
% 0.13/0.37  % Mode: mode213
% 0.13/0.37  % Inferences: 105
% 0.13/0.37  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------