%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SYO267^5 : 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 : n013.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 : Fri Sep  1 04:46:05 EDT 2023

% Result   : Theorem 0.19s 0.39s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

thf(sP1,plain,
    ( sP1
  <=> ! [X1: ( $i > $i ) > $o] :
        ~ ! [X2: $i > $i,X3: $i > $i] :
            ( ~ ( ( X1 @ X2 )
               => ~ ( X1 @ X3 ) )
           => ~ ( ( X1
                  @ ^ [X4: $i] : ( X2 @ ( X3 @ X4 ) ) )
               => ~ ! [X4: $i] :
                      ( ( eigen__0 @ X4 )
                     => ( eigen__0 @ ( X2 @ X4 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(cTHM111,conjecture,
    ! [X1: $i > $o] :
      ~ ! [X2: ( $i > $i ) > $o] :
          ~ ! [X3: $i > $i,X4: $i > $i] :
              ( ~ ( ( X2 @ X3 )
                 => ~ ( X2 @ X4 ) )
             => ~ ( ( X2
                    @ ^ [X5: $i] : ( X3 @ ( X4 @ X5 ) ) )
                 => ~ ! [X5: $i] :
                        ( ( X1 @ X5 )
                       => ( X1 @ ( X3 @ X5 ) ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: $i > $o] :
        ~ ! [X2: ( $i > $i ) > $o] :
            ~ ! [X3: $i > $i,X4: $i > $i] :
                ( ~ ( ( X2 @ X3 )
                   => ~ ( X2 @ X4 ) )
               => ~ ( ( X2
                      @ ^ [X5: $i] : ( X3 @ ( X4 @ X5 ) ) )
                   => ~ ! [X5: $i] :
                          ( ( X1 @ X5 )
                         => ( X1 @ ( X3 @ X5 ) ) ) ) ),
    inference(assume_negation,[status(cth)],[cTHM111]) ).

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

thf(1,plain,
    ~ sP2,
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP1
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

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

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: $i > $o] :
      ~ ! [X2: ( $i > $i ) > $o] :
          ~ ! [X3: $i > $i,X4: $i > $i] :
              ( ~ ( ( X2 @ X3 )
                 => ~ ( X2 @ X4 ) )
             => ~ ( ( X2
                    @ ^ [X5: $i] : ( X3 @ ( X4 @ X5 ) ) )
                 => ~ ! [X5: $i] :
                        ( ( X1 @ X5 )
                       => ( X1 @ ( X3 @ X5 ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[4,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SYO267^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n013.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Sat Aug 26 07:25:47 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.39  % SZS status Theorem
% 0.19/0.39  % Mode: cade22grackle2xfee4
% 0.19/0.39  % Steps: 25
% 0.19/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------