%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : PUZ102^5 : TPTP v8.1.2. Bugfixed v5.2.0.
% 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 : Thu Aug 31 13:21:52 EDT 2023

% Result   : Theorem 0.20s 0.41s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

thf(ty_s,type,
    s: $i > $i ).

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

thf(sP1,plain,
    ( sP1
  <=> ! [X1: $i] :
        ( ( eigen__1 @ X1 )
       => ( eigen__1 @ ( s @ ( s @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( eigen__1 @ eigen__0 )
     => ( eigen__1 @ ( s @ ( s @ eigen__0 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( eigen__1 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

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

thf(def_cCKB_E2,definition,
    ( cCKB_E2
    = ( ^ [X1: $i,X2: $i] :
        ! [X3: $i > $o] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( ( X3 @ X1 )
            & ! [X4: $i] :
                ( ^ [X5: $o,X6: $o] :
                    ( X5
                   => X6 )
                @ ( X3 @ X4 )
                @ ( X3 @ ( s @ ( s @ X4 ) ) ) ) )
          @ ( X3 @ X2 ) ) ) ) ).

thf(cCKB_L33000,conjecture,
    ! [X1: $i,X2: $i > $o] :
      ( ~ ( ( X2 @ X1 )
         => ~ ! [X3: $i] :
                ( ( X2 @ X3 )
               => ( X2 @ ( s @ ( s @ X3 ) ) ) ) )
     => ( X2 @ ( s @ ( s @ X1 ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: $i,X2: $i > $o] :
        ( ~ ( ( X2 @ X1 )
           => ~ ! [X3: $i] :
                  ( ( X2 @ X3 )
                 => ( X2 @ ( s @ ( s @ X3 ) ) ) ) )
       => ( X2 @ ( s @ ( s @ X1 ) ) ) ),
    inference(assume_negation,[status(cth)],[cCKB_L33000]) ).

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

thf(h2,assumption,
    ~ ( ~ ( sP3
         => ~ sP1 )
     => sP4 ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ( sP3
     => ~ sP1 ),
    introduced(assumption,[]) ).

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

thf(h5,assumption,
    sP3,
    introduced(assumption,[]) ).

thf(h6,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP2
    | ~ sP3
    | sP4 ),
    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([h5,h6,h3,h4,h2,h1,h0])],[1,2,h5,h6,h4]) ).

thf(4,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h3,3,h5,h6]) ).

thf(5,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,4,h3,h4]) ).

thf(6,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,5,h2]) ).

thf(7,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,6,h1]) ).

thf(0,theorem,
    ! [X1: $i,X2: $i > $o] :
      ( ~ ( ( X2 @ X1 )
         => ~ ! [X3: $i] :
                ( ( X2 @ X3 )
               => ( X2 @ ( s @ ( s @ X3 ) ) ) ) )
     => ( X2 @ ( s @ ( s @ X1 ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[7,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : PUZ102^5 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.12/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n013.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  : 300
% 0.13/0.34  % DateTime : Sat Aug 26 22:23:32 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.41  % SZS status Theorem
% 0.20/0.41  % Mode: cade22grackle2xfee4
% 0.20/0.41  % Steps: 8
% 0.20/0.41  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------