%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : PUZ081^2 : TPTP v8.1.2. Bugfixed v7.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n003.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 13:21:47 EDT 2023

% Result   : Theorem 0.20s 0.63s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_zoey,type,
    zoey: $i ).

thf(ty_knight,type,
    knight: $i > $o ).

thf(ty_mel,type,
    mel: $i ).

thf(ty_knave,type,
    knave: $i > $o ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: $i > $o] :
        ( ~ ( ( ( X1 != knight )
             => ( X1 = knave ) )
           => ~ ( knight @ zoey ) )
       => ~ ( X1 @ mel ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( knight @ mel ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

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

thf(sP4,plain,
    ( sP4
  <=> ( ( knight @ zoey )
      = ( knave @ zoey ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( knave @ mel ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( knight @ zoey ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( sP6
     => ~ sP5 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( knave @ zoey ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ! [X1: $i] :
        ( ( knight @ X1 )
       != ( knave @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( sP6
     => ~ sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ! [X1: $i > $o] :
        ( ~ ( ( ( X1 != knight )
             => ( X1 = knave ) )
           => ~ sP8 )
       => ~ ( X1 @ mel ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( sP2 = sP5 ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( sP8
     => ~ sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( sP8
     => ~ sP5 ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(what_are_zoey_and_mel,conjecture,
    ~ sP3 ).

thf(h0,negated_conjecture,
    sP3,
    inference(assume_negation,[status(cth)],[what_are_zoey_and_mel]) ).

thf(1,plain,
    ( sP12
    | sP2
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP9
    | ~ sP12 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP4
    | sP6
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP9
    | ~ sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP13
    | ~ sP8
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP14
    | ~ sP8
    | ~ sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP11
    | sP13 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP11
    | sP14 ),
    inference(all_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP7
    | ~ sP6
    | ~ sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP3
    | sP11 ),
    inference(all_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP1
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP10
    | ~ sP6
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP1
    | sP10 ),
    inference(all_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP3
    | sP1 ),
    inference(all_rule,[status(thm)],]) ).

thf(knights_xor_knaves,axiom,
    sP9 ).

thf(15,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,h0,knights_xor_knaves]) ).

thf(0,theorem,
    ~ sP3,
    inference(contra,[status(thm),contra(discharge,[h0])],[15,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : PUZ081^2 : TPTP v8.1.2. Bugfixed v7.1.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34  % Computer : n003.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % 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 22:13:24 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.20/0.63  % SZS status Theorem
% 0.20/0.63  % Mode: cade22grackle2xfee4
% 0.20/0.63  % Steps: 2597
% 0.20/0.63  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------