%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEU858^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n007.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  : 300s
% DateTime : Thu Aug 31 17:37:41 EDT 2023

% Result   : Theorem 0.21s 0.40s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

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

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

thf(cTHM163_pme,conjecture,
    ! [X1: ( a > $o ) > $o] :
      ( ~ ( ( X1
            @ ^ [X2: a] : $false )
         => ~ ! [X2: a > $o,X3: a] :
                ( ( X1 @ X2 )
               => ( X1
                  @ ^ [X4: a] :
                      ( ~ ( X2 @ X4 )
                     => ( X4 = X3 ) ) ) ) )
     => ( X1
        @ ^ [X2: a] : $false ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: ( a > $o ) > $o] :
        ( ~ ( ( X1
              @ ^ [X2: a] : $false )
           => ~ ! [X2: a > $o,X3: a] :
                  ( ( X1 @ X2 )
                 => ( X1
                    @ ^ [X4: a] :
                        ( ~ ( X2 @ X4 )
                       => ( X4 = X3 ) ) ) ) )
       => ( X1
          @ ^ [X2: a] : $false ) ),
    inference(assume_negation,[status(cth)],[cTHM163_pme]) ).

thf(h1,assumption,
    ~ ( ~ ( sP1
         => ~ ! [X1: a > $o,X2: a] :
                ( ( eigen__0 @ X1 )
               => ( eigen__0
                  @ ^ [X3: a] :
                      ( ~ ( X1 @ X3 )
                     => ( X3 = X2 ) ) ) ) )
     => sP1 ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ( sP1
     => ~ ! [X1: a > $o,X2: a] :
            ( ( eigen__0 @ X1 )
           => ( eigen__0
              @ ^ [X3: a] :
                  ( ~ ( X1 @ X3 )
                 => ( X3 = X2 ) ) ) ) ),
    introduced(assumption,[]) ).

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

thf(h4,assumption,
    sP1,
    introduced(assumption,[]) ).

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

thf(1,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h4,h5,h2,h3,h1,h0])],[h4,h3]) ).

thf(2,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,1,h4,h5]) ).

thf(3,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,2,h2,h3]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : SEU858^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.16/0.36  % Computer : n007.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Wed Aug 23 19:06:24 EDT 2023
% 0.16/0.36  % CPUTime  : 
% 0.21/0.40  % SZS status Theorem
% 0.21/0.40  % Mode: cade22grackle2xfee4
% 0.21/0.40  % Steps: 0
% 0.21/0.40  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------