%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEV122^5 : 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 : n015.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 18:04:57 EDT 2022

% Result   : Theorem 0.14s 0.37s
% Output   : Proof 0.14s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

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

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

thf(cTHM530_pme,conjecture,
    ! [X1: ( a > a > $o ) > $o,X2: ( a > a > $o ) > $o] :
      ( ( ^ [X3: a,X4: a] :
          ! [X5: a > a > $o] :
            ( ~ ( ! [X6: a,X7: a] :
                    ( ~ ! [X8: a > a > $o] :
                          ~ ( X8 @ X6 @ X7 )
                   => ( X5 @ X6 @ X7 ) )
               => ~ ( X1 @ X5 ) )
           => ( X5 @ X3 @ X4 ) ) )
      = ( ^ [X3: a,X4: a] :
          ! [X5: a > a > $o] :
            ( ~ ( ! [X6: a,X7: a] :
                    ( ~ ! [X8: a > a > $o] :
                          ~ ( X8 @ X6 @ X7 )
                   => ( X5 @ X6 @ X7 ) )
               => ~ ( X1 @ X5 ) )
           => ( X5 @ X3 @ X4 ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: ( a > a > $o ) > $o,X2: ( a > a > $o ) > $o] :
        ( ( ^ [X3: a,X4: a] :
            ! [X5: a > a > $o] :
              ( ~ ( ! [X6: a,X7: a] :
                      ( ~ ! [X8: a > a > $o] :
                            ~ ( X8 @ X6 @ X7 )
                     => ( X5 @ X6 @ X7 ) )
                 => ~ ( X1 @ X5 ) )
             => ( X5 @ X3 @ X4 ) ) )
        = ( ^ [X3: a,X4: a] :
            ! [X5: a > a > $o] :
              ( ~ ( ! [X6: a,X7: a] :
                      ( ~ ! [X8: a > a > $o] :
                            ~ ( X8 @ X6 @ X7 )
                     => ( X5 @ X6 @ X7 ) )
                 => ~ ( X1 @ X5 ) )
             => ( X5 @ X3 @ X4 ) ) ) ),
    inference(assume_negation,[status(cth)],[cTHM530_pme]) ).

thf(h1,assumption,
    ~ ! [X1: ( a > a > $o ) > $o] :
        ( ( ^ [X2: a,X3: a] :
            ! [X4: a > a > $o] :
              ( ~ ( ! [X5: a,X6: a] :
                      ( ~ ! [X7: a > a > $o] :
                            ~ ( X7 @ X5 @ X6 )
                     => ( X4 @ X5 @ X6 ) )
                 => ~ ( eigen__0 @ X4 ) )
             => ( X4 @ X2 @ X3 ) ) )
        = ( ^ [X2: a,X3: a] :
            ! [X4: a > a > $o] :
              ( ~ ( ! [X5: a,X6: a] :
                      ( ~ ! [X7: a > a > $o] :
                            ~ ( X7 @ X5 @ X6 )
                     => ( X4 @ X5 @ X6 ) )
                 => ~ ( eigen__0 @ X4 ) )
             => ( X4 @ X2 @ X3 ) ) ) ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ( ^ [X1: a,X2: a] :
      ! [X3: a > a > $o] :
        ( ~ ( ! [X4: a,X5: a] :
                ( ~ ! [X6: a > a > $o] :
                      ~ ( X6 @ X4 @ X5 )
               => ( X3 @ X4 @ X5 ) )
           => ~ ( eigen__0 @ X3 ) )
       => ( X3 @ X1 @ X2 ) ) )
 != ( ^ [X1: a,X2: a] :
      ! [X3: a > a > $o] :
        ( ~ ( ! [X4: a,X5: a] :
                ( ~ ! [X6: a > a > $o] :
                      ~ ( X6 @ X4 @ X5 )
               => ( X3 @ X4 @ X5 ) )
           => ~ ( eigen__0 @ X3 ) )
       => ( X3 @ X1 @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(1,plain,
    $false,
    inference(tab_negrefl,[status(thm),assumptions([h2,h1,h0])],[h2]) ).

thf(2,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,1,h2]) ).

thf(3,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,2,h1]) ).

thf(0,theorem,
    ! [X1: ( a > a > $o ) > $o,X2: ( a > a > $o ) > $o] :
      ( ( ^ [X3: a,X4: a] :
          ! [X5: a > a > $o] :
            ( ~ ( ! [X6: a,X7: a] :
                    ( ~ ! [X8: a > a > $o] :
                          ~ ( X8 @ X6 @ X7 )
                   => ( X5 @ X6 @ X7 ) )
               => ~ ( X1 @ X5 ) )
           => ( X5 @ X3 @ X4 ) ) )
      = ( ^ [X3: a,X4: a] :
          ! [X5: a > a > $o] :
            ( ~ ( ! [X6: a,X7: a] :
                    ( ~ ! [X8: a > a > $o] :
                          ~ ( X8 @ X6 @ X7 )
                   => ( X5 @ X6 @ X7 ) )
               => ~ ( X1 @ X5 ) )
           => ( X5 @ X3 @ X4 ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[3,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SEV122^5 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35  % Computer : n015.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Tue Jun 28 15:36:55 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.14/0.37  % SZS status Theorem
% 0.14/0.37  % Mode: mode213
% 0.14/0.37  % Inferences: 0
% 0.14/0.37  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------