%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEV014^5 : 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 : n011.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 18:04:27 EDT 2022

% Result   : Theorem 0.12s 0.35s
% Output   : Proof 0.12s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

thf(ty_eigen__1,type,
    eigen__1: a ).

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

thf(sP1,plain,
    ( sP1
  <=> ( eigen__0 @ eigen__1 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

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

thf(cTHM513_pme,conjecture,
    ! [X1: a > a > $o] :
      ( ~ ( ~ ( ! [X2: a] : ( X1 @ X2 @ X2 )
             => ~ ! [X2: a,X3: a] :
                    ( ( X1 @ X2 @ X3 )
                   => ( X1 @ X3 @ X2 ) ) )
         => ~ ! [X2: a,X3: a,X4: a] :
                ( ~ ( ( X1 @ X2 @ X3 )
                   => ~ ( X1 @ X3 @ X4 ) )
               => ( X1 @ X2 @ X4 ) ) )
     => ! [X2: a] : ( X1 @ X2 @ X2 ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: a > a > $o] :
        ( ~ ( ~ ( ! [X2: a] : ( X1 @ X2 @ X2 )
               => ~ ! [X2: a,X3: a] :
                      ( ( X1 @ X2 @ X3 )
                     => ( X1 @ X3 @ X2 ) ) )
           => ~ ! [X2: a,X3: a,X4: a] :
                  ( ~ ( ( X1 @ X2 @ X3 )
                     => ~ ( X1 @ X3 @ X4 ) )
                 => ( X1 @ X2 @ X4 ) ) )
       => ! [X2: a] : ( X1 @ X2 @ X2 ) ),
    inference(assume_negation,[status(cth)],[cTHM513_pme]) ).

thf(h1,assumption,
    ~ ( ~ ( ~ ( sP2
             => ~ ! [X1: a,X2: a] :
                    ( ( eigen__0 @ X1 @ X2 )
                   => ( eigen__0 @ X2 @ X1 ) ) )
         => ~ ! [X1: a,X2: a,X3: a] :
                ( ~ ( ( eigen__0 @ X1 @ X2 )
                   => ~ ( eigen__0 @ X2 @ X3 ) )
               => ( eigen__0 @ X1 @ X3 ) ) )
     => sP2 ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ( ~ ( sP2
         => ~ ! [X1: a,X2: a] :
                ( ( eigen__0 @ X1 @ X2 )
               => ( eigen__0 @ X2 @ X1 ) ) )
     => ~ ! [X1: a,X2: a,X3: a] :
            ( ~ ( ( eigen__0 @ X1 @ X2 )
               => ~ ( eigen__0 @ X2 @ X3 ) )
           => ( eigen__0 @ X1 @ X3 ) ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ sP2,
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ( sP2
     => ~ ! [X1: a,X2: a] :
            ( ( eigen__0 @ X1 @ X2 )
           => ( eigen__0 @ X2 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    ! [X1: a,X2: a,X3: a] :
      ( ~ ( ( eigen__0 @ X1 @ X2 )
         => ~ ( eigen__0 @ X2 @ X3 ) )
     => ( eigen__0 @ X1 @ X3 ) ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    sP2,
    introduced(assumption,[]) ).

thf(h7,assumption,
    ! [X1: a,X2: a] :
      ( ( eigen__0 @ X1 @ X2 )
     => ( eigen__0 @ X2 @ X1 ) ),
    introduced(assumption,[]) ).

thf(h8,assumption,
    ~ sP1,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP2
    | sP1 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h8,h6,h7,h4,h5,h2,h3,h1,h0])],[1,h6,h8]) ).

thf(3,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__1)],[h3,2,h8]) ).

thf(4,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,3,h6,h7]) ).

thf(5,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,4,h4,h5]) ).

thf(6,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,5,h2,h3]) ).

thf(7,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,6,h1]) ).

thf(0,theorem,
    ! [X1: a > a > $o] :
      ( ~ ( ~ ( ! [X2: a] : ( X1 @ X2 @ X2 )
             => ~ ! [X2: a,X3: a] :
                    ( ( X1 @ X2 @ X3 )
                   => ( X1 @ X3 @ X2 ) ) )
         => ~ ! [X2: a,X3: a,X4: a] :
                ( ~ ( ( X1 @ X2 @ X3 )
                   => ~ ( X1 @ X3 @ X4 ) )
               => ( X1 @ X2 @ X4 ) ) )
     => ! [X2: a] : ( X1 @ X2 @ X2 ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[7,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEV014^5 : 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 : n011.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 : Tue Jun 28 17:09:46 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.35  % SZS status Theorem
% 0.12/0.35  % Mode: mode213
% 0.12/0.35  % Inferences: 4
% 0.12/0.35  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------