%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEV177^5 : 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 : n010.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 0.14s 0.41s
% Output   : Proof 0.14s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
    eigen__1: $i > $o ).

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

thf(sP1,plain,
    ( sP1
  <=> ( eigen__1
      = ( ^ [X1: $i] :
            ~ ! [X2: $i > $o] :
                ( ~ ( X2 @ ( eigen__0 @ X2 ) )
               => ( X1
                 != ( eigen__0 @ X2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: $i > $o] :
        ( ~ ( X1 @ ( eigen__0 @ X1 ) )
       => ( ( eigen__0 @ eigen__1 )
         != ( eigen__0 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: $i] :
        ( ( eigen__1 @ X1 )
        = ( ~ ! [X2: $i > $o] :
                ( ~ ( X2 @ ( eigen__0 @ X2 ) )
               => ( X1
                 != ( eigen__0 @ X2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( eigen__1 @ ( eigen__0 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( sP4 = ~ sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(cTHM144_pme,conjecture,
    ! [X1: ( $i > $o ) > $i,X2: $i > $o] :
      ( ( X2
        = ( ^ [X3: $i] :
              ~ ! [X4: $i > $o] :
                  ( ~ ( X4 @ ( X1 @ X4 ) )
                 => ( X3
                   != ( X1 @ X4 ) ) ) ) )
     => ( X2 @ ( X1 @ X2 ) ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: ( $i > $o ) > $i,X2: $i > $o] :
        ( ( X2
          = ( ^ [X3: $i] :
                ~ ! [X4: $i > $o] :
                    ( ~ ( X4 @ ( X1 @ X4 ) )
                   => ( X3
                     != ( X1 @ X4 ) ) ) ) )
       => ( X2 @ ( X1 @ X2 ) ) ),
    inference(assume_negation,[status(cth)],[cTHM144_pme]) ).

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

thf(h2,assumption,
    ~ ( sP1
     => sP4 ),
    introduced(assumption,[]) ).

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

thf(h4,assumption,
    ~ sP4,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP2
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP5
    | sP4
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP3
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP1
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h3,h4,h2,h1,h0])],[1,2,3,4,h3,h4]) ).

thf(6,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,5,h3,h4]) ).

thf(7,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,6,h2]) ).

thf(8,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,7,h1]) ).

thf(0,theorem,
    ! [X1: ( $i > $o ) > $i,X2: $i > $o] :
      ( ( X2
        = ( ^ [X3: $i] :
              ~ ! [X4: $i > $o] :
                  ( ~ ( X4 @ ( X1 @ X4 ) )
                 => ( X3
                   != ( X1 @ X4 ) ) ) ) )
     => ( X2 @ ( X1 @ X2 ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[8,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEV177^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35  % Computer : n010.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  : 300
% 0.14/0.35  % DateTime : Thu Aug 24 03:33:51 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.14/0.41  % SZS status Theorem
% 0.14/0.41  % Mode: cade22grackle2xfee4
% 0.14/0.41  % Steps: 10
% 0.14/0.41  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------