%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SYO022^1 : TPTP v8.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n021.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 19:29:36 EDT 2022

% Result   : Theorem 0.20s 0.36s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

thf(sP1,plain,
    ( sP1
  <=> ( eigen__0
      @ ^ [X1: $o,X2: $o] :
          ~ ( X1
           => ~ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(def_leibeq,definition,
    ( leibeq
    = ( ^ [X1: $o > $o > $o,X2: $o > $o > $o] :
        ! [X3: ( $o > $o > $o ) > $o] :
          ( ( X3 @ X1 )
         => ( X3 @ X2 ) ) ) ) ).

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

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

thf(h1,assumption,
    ~ ( sP1
     => sP1 ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ sP1,
    introduced(assumption,[]) ).

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

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

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: ( $o > $o > $o ) > $o] :
      ( ( X1
        @ ^ [X2: $o,X3: $o] :
            ~ ( X2
             => ~ X3 ) )
     => ( X1
        @ ^ [X2: $o,X3: $o] :
            ~ ( X2
             => ~ X3 ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[3,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SYO022^1 : TPTP v8.1.0. Released v3.7.0.
% 0.03/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n021.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 14:40:21 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.36  % SZS status Theorem
% 0.20/0.36  % Mode: mode213
% 0.20/0.36  % Inferences: 0
% 0.20/0.36  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------