%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SET159^5 : 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 : n026.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 04:51:40 EDT 2022

% Result   : Theorem 0.13s 0.35s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

thf(ty_eigen__2,type,
    eigen__2: a > $o ).

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

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

thf(cBOOL_PROP_64_pme,conjecture,
    ! [X1: a > $o,X2: a > $o,X3: a > $o] :
      ( ( ^ [X4: a] :
            ( ~ ( ~ ( X1 @ X4 )
               => ( X2 @ X4 ) )
           => ( X3 @ X4 ) ) )
      = ( ^ [X4: a] :
            ( ~ ( ~ ( X1 @ X4 )
               => ( X2 @ X4 ) )
           => ( X3 @ X4 ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: a > $o,X2: a > $o,X3: a > $o] :
        ( ( ^ [X4: a] :
              ( ~ ( ~ ( X1 @ X4 )
                 => ( X2 @ X4 ) )
             => ( X3 @ X4 ) ) )
        = ( ^ [X4: a] :
              ( ~ ( ~ ( X1 @ X4 )
                 => ( X2 @ X4 ) )
             => ( X3 @ X4 ) ) ) ),
    inference(assume_negation,[status(cth)],[cBOOL_PROP_64_pme]) ).

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

thf(h2,assumption,
    ~ ! [X1: a > $o] :
        ( ( ^ [X2: a] :
              ( ~ ( ~ ( eigen__0 @ X2 )
                 => ( eigen__1 @ X2 ) )
             => ( X1 @ X2 ) ) )
        = ( ^ [X2: a] :
              ( ~ ( ~ ( eigen__0 @ X2 )
                 => ( eigen__1 @ X2 ) )
             => ( X1 @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ( ^ [X1: a] :
        ( ~ ( ~ ( eigen__0 @ X1 )
           => ( eigen__1 @ X1 ) )
       => ( eigen__2 @ X1 ) ) )
 != ( ^ [X1: a] :
        ( ~ ( ~ ( eigen__0 @ X1 )
           => ( eigen__1 @ X1 ) )
       => ( eigen__2 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(1,plain,
    $false,
    inference(tab_negrefl,[status(thm),assumptions([h3,h2,h1,h0])],[h3]) ).

thf(2,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,1,h3]) ).

thf(3,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,2,h2]) ).

thf(4,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,3,h1]) ).

thf(0,theorem,
    ! [X1: a > $o,X2: a > $o,X3: a > $o] :
      ( ( ^ [X4: a] :
            ( ~ ( ~ ( X1 @ X4 )
               => ( X2 @ X4 ) )
           => ( X3 @ X4 ) ) )
      = ( ^ [X4: a] :
            ( ~ ( ~ ( X1 @ X4 )
               => ( X2 @ X4 ) )
           => ( X3 @ X4 ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[4,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET159^5 : 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
% 0.13/0.33  % Computer : n026.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sun Jul 10 01:28:56 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.35  % SZS status Theorem
% 0.13/0.35  % Mode: mode213
% 0.13/0.35  % Inferences: 0
% 0.13/0.35  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------