%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEV175^5 : 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 : n027.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 19:32:51 EDT 2023

% Result   : Theorem 0.16s 0.35s
% Output   : Proof 0.16s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

thf(sP1,plain,
    ( sP1
  <=> ! [X1: $i > $o] :
        ( ~ ( X1 @ ( eigen__0 @ X1 ) )
       => ( ( eigen__0
            @ ^ [X2: $i] :
                ~ ! [X3: $i > $o] :
                    ( ~ ( X3 @ ( eigen__0 @ X3 ) )
                   => ( X2
                     != ( eigen__0 @ X3 ) ) ) )
         != ( eigen__0 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(cTHM144A_pme,conjecture,
    ! [X1: ( $i > $o ) > $i] :
      ~ ! [X2: $i > $o] :
          ( ~ ( X2 @ ( X1 @ X2 ) )
         => ( ( X1
              @ ^ [X3: $i] :
                  ~ ! [X4: $i > $o] :
                      ( ~ ( X4 @ ( X1 @ X4 ) )
                     => ( X3
                       != ( X1 @ X4 ) ) ) )
           != ( X1 @ X2 ) ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: ( $i > $o ) > $i] :
        ~ ! [X2: $i > $o] :
            ( ~ ( X2 @ ( X1 @ X2 ) )
           => ( ( X1
                @ ^ [X3: $i] :
                    ~ ! [X4: $i > $o] :
                        ( ~ ( X4 @ ( X1 @ X4 ) )
                       => ( X3
                         != ( X1 @ X4 ) ) ) )
             != ( X1 @ X2 ) ) ),
    inference(assume_negation,[status(cth)],[cTHM144A_pme]) ).

thf(h1,assumption,
    sP1,
    introduced(assumption,[]) ).

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

thf(2,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,h1]) ).

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: ( $i > $o ) > $i] :
      ~ ! [X2: $i > $o] :
          ( ~ ( X2 @ ( X1 @ X2 ) )
         => ( ( X1
              @ ^ [X3: $i] :
                  ~ ! [X4: $i > $o] :
                      ( ~ ( X4 @ ( X1 @ X4 ) )
                     => ( X3
                       != ( X1 @ X4 ) ) ) )
           != ( X1 @ X2 ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[3,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SEV175^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.11  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.11/0.31  % Computer : n027.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Thu Aug 24 03:58:47 EDT 2023
% 0.11/0.31  % CPUTime  : 
% 0.16/0.35  % SZS status Theorem
% 0.16/0.35  % Mode: cade22grackle2xfee4
% 0.16/0.35  % Steps: 3
% 0.16/0.35  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------