%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SET043^5 : 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 : n006.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 04:50:15 EDT 2022

% Result   : Theorem 0.12s 0.36s
% Output   : Proof 0.12s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

thf(ty_cE,type,
    cE: $i > $i > $o ).

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

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

thf(sP3,plain,
    ( sP3
  <=> ( cE @ eigen__0 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(cRUSSELL1,conjecture,
    ! [X1: $i] :
      ~ ! [X2: $i] :
          ( ( cE @ X2 @ X1 )
          = ( ~ ( cE @ X2 @ X2 ) ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: $i] :
        ~ ! [X2: $i] :
            ( ( cE @ X2 @ X1 )
            = ( ~ ( cE @ X2 @ X2 ) ) ),
    inference(assume_negation,[status(cth)],[cRUSSELL1]) ).

thf(h1,assumption,
    sP2,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP1
    | ~ sP3
    | ~ sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP1
    | sP3
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

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

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

thf(5,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,4,h1]) ).

thf(0,theorem,
    ! [X1: $i] :
      ~ ! [X2: $i] :
          ( ( cE @ X2 @ X1 )
          = ( ~ ( cE @ X2 @ X2 ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[5,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET043^5 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n006.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 : Mon Jul 11 09:29:50 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.36  % SZS status Theorem
% 0.12/0.36  % Mode: mode213
% 0.12/0.36  % Inferences: 13
% 0.12/0.36  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------