TSTP Solution File: PUZ081^1 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : PUZ081^1 : TPTP v8.1.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -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  : 600s
% DateTime : Mon Jul 18 18:24:41 EDT 2022

% Result   : Theorem 25.80s 26.03s
% Output   : Proof 25.80s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_knave,type,
    knave: $i ).

thf(ty_is_a,type,
    is_a: $i > $i > $o ).

thf(ty_islander,type,
    islander: $i ).

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

thf(ty_says,type,
    says: $i > $o > $o ).

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

thf(ty_zoey,type,
    zoey: $i ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: $i] :
        ( ( is_a @ X1 @ knight )
       => ! [X2: $o] :
            ( ( says @ X1 @ X2 )
           => X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

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

thf(sP3,plain,
    ( sP3
  <=> ( says @ mel
      @ ~ ( ~ ( is_a @ zoey @ knave )
         => ( is_a @ mel @ knave ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ~ sP2
     => ( is_a @ zoey @ knave ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

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

thf(sP6,plain,
    ( sP6
  <=> ( ~ ( is_a @ mel @ knight )
     => ( is_a @ mel @ knave ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( is_a @ zoey @ islander ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ~ sP5
     => ~ ( is_a @ mel @ knave ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ! [X1: $o] :
        ( ( says @ zoey @ X1 )
       => X1 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( knight = knave ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( knight = knight ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( ( is_a @ mel @ islander )
     => sP6 ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( ( is_a @ mel @ knight )
     => ! [X1: $o] :
          ( ( says @ mel @ X1 )
         => X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( says @ zoey @ ( is_a @ mel @ knave ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( ( knave = knight )
     => sP10 ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( sP11 = sP10 ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( sP7
     => sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ( ( knave = knight )
      = ( knave = knave ) ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ( sP14
     => ~ ( is_a @ mel @ knave ) ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ( is_a @ mel @ knave ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ! [X1: $o] :
        ( ( says @ mel @ X1 )
       => X1 ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ( sP14
     => sP20 ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ( is_a @ mel @ knight ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> ( ~ ( is_a @ zoey @ knave )
     => sP20 ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ! [X1: $i] :
        ( ( is_a @ X1 @ knave )
       => ! [X2: $o] :
            ( ( says @ X1 @ X2 )
           => ~ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
    ( sP26
  <=> ( sP2
     => sP9 ) ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
    ( sP27
  <=> ! [X1: $i] :
        ( ( is_a @ X1 @ islander )
       => ( ~ ( is_a @ X1 @ knight )
         => ( is_a @ X1 @ knave ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP27])]) ).

thf(sP28,plain,
    ( sP28
  <=> ( knave = knight ) ),
    introduced(definition,[new_symbols(definition,[sP28])]) ).

thf(sP29,plain,
    ( sP29
  <=> ! [X1: $i,X2: $i] :
        ( ~ ( ~ ( ( ( X1 = knight )
                 != ( X1 = knave ) )
               => ( ( X2 = knight )
                  = ( X2 = knave ) ) )
           => ~ ( is_a @ mel @ X1 ) )
       => ~ ( is_a @ zoey @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP29])]) ).

thf(sP30,plain,
    ( sP30
  <=> ( is_a @ zoey @ knave ) ),
    introduced(definition,[new_symbols(definition,[sP30])]) ).

thf(sP31,plain,
    ( sP31
  <=> ( ~ sP8
     => ~ sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP31])]) ).

thf(sP32,plain,
    ( sP32
  <=> ( zoey = zoey ) ),
    introduced(definition,[new_symbols(definition,[sP32])]) ).

thf(sP33,plain,
    ( sP33
  <=> ( sP30
     => ! [X1: $o] :
          ( ( says @ zoey @ X1 )
         => ~ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP33])]) ).

thf(sP34,plain,
    ( sP34
  <=> ( knave = knave ) ),
    introduced(definition,[new_symbols(definition,[sP34])]) ).

thf(sP35,plain,
    ( sP35
  <=> ! [X1: $o] :
        ( ( says @ zoey @ X1 )
       => ~ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP35])]) ).

thf(sP36,plain,
    ( sP36
  <=> ! [X1: $i] :
        ( ~ ( ~ ( ~ sP18
               => ( ( X1 = knight )
                  = ( X1 = knave ) ) )
           => ~ sP20 )
       => ~ ( is_a @ zoey @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP36])]) ).

thf(sP37,plain,
    ( sP37
  <=> ! [X1: $i,X2: $i] :
        ( ( X1 = X2 )
       => ( X2 = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP37])]) ).

thf(sP38,plain,
    ( sP38
  <=> ( is_a @ mel @ islander ) ),
    introduced(definition,[new_symbols(definition,[sP38])]) ).

thf(sP39,plain,
    ( sP39
  <=> ! [X1: $i] :
        ( ( knave = X1 )
       => ( X1 = knave ) ) ),
    introduced(definition,[new_symbols(definition,[sP39])]) ).

thf(sP40,plain,
    ( sP40
  <=> ( sP3
     => ~ sP24 ) ),
    introduced(definition,[new_symbols(definition,[sP40])]) ).

thf(query,conjecture,
    ~ sP29 ).

thf(h0,negated_conjecture,
    sP29,
    inference(assume_negation,[status(cth)],[query]) ).

thf(h1,assumption,
    sP7,
    introduced(assumption,[]) ).

thf(h2,assumption,
    sP38,
    introduced(assumption,[]) ).

thf(1,plain,
    sP11,
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP15
    | ~ sP28
    | sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP39
    | sP15 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    sP32,
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    sP34,
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP37
    | sP39 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    sP37,
    inference(eq_sym,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP2
    | sP30
    | ~ sP32
    | ~ sP10 ),
    inference(mating_rule,[status(thm)],]) ).

thf(9,plain,
    ( sP24
    | ~ sP30 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP36
    | sP31 ),
    inference(all_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP31
    | sP8
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP8
    | sP5
    | ~ sP20 ),
    inference(prop_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP5
    | sP18
    | sP16 ),
    inference(prop_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP18
    | sP28
    | ~ sP34 ),
    inference(prop_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP16
    | ~ sP11
    | sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(16,plain,
    ( ~ sP27
    | sP17 ),
    inference(all_rule,[status(thm)],]) ).

thf(17,plain,
    ( ~ sP17
    | ~ sP7
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP4
    | sP2
    | sP30 ),
    inference(prop_rule,[status(thm)],]) ).

thf(19,plain,
    ( ~ sP27
    | sP12 ),
    inference(all_rule,[status(thm)],]) ).

thf(20,plain,
    ( ~ sP12
    | ~ sP38
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(21,plain,
    ( ~ sP6
    | sP23
    | sP20 ),
    inference(prop_rule,[status(thm)],]) ).

thf(22,plain,
    ( ~ sP29
    | sP36 ),
    inference(all_rule,[status(thm)],]) ).

thf(23,plain,
    ( ~ sP1
    | sP13 ),
    inference(all_rule,[status(thm)],]) ).

thf(24,plain,
    ( ~ sP13
    | ~ sP23
    | sP21 ),
    inference(prop_rule,[status(thm)],]) ).

thf(25,plain,
    ( ~ sP21
    | sP40 ),
    inference(all_rule,[status(thm)],]) ).

thf(26,plain,
    ( ~ sP40
    | ~ sP3
    | ~ sP24 ),
    inference(prop_rule,[status(thm)],]) ).

thf(27,plain,
    ( ~ sP1
    | sP26 ),
    inference(all_rule,[status(thm)],]) ).

thf(28,plain,
    ( ~ sP26
    | ~ sP2
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(29,plain,
    ( ~ sP9
    | sP22 ),
    inference(all_rule,[status(thm)],]) ).

thf(30,plain,
    ( ~ sP22
    | ~ sP14
    | sP20 ),
    inference(prop_rule,[status(thm)],]) ).

thf(31,plain,
    ( ~ sP25
    | sP33 ),
    inference(all_rule,[status(thm)],]) ).

thf(32,plain,
    ( ~ sP33
    | ~ sP30
    | sP35 ),
    inference(prop_rule,[status(thm)],]) ).

thf(33,plain,
    ( ~ sP35
    | sP19 ),
    inference(all_rule,[status(thm)],]) ).

thf(34,plain,
    ( ~ sP19
    | ~ sP14
    | ~ sP20 ),
    inference(prop_rule,[status(thm)],]) ).

thf(kk_6_6,axiom,
    sP3 ).

thf(kk_6_5,axiom,
    sP14 ).

thf(kk_6_3,axiom,
    sP25 ).

thf(kk_6_2,axiom,
    sP1 ).

thf(kk_6_1,axiom,
    sP27 ).

thf(35,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,h0,kk_6_6,kk_6_5,h1,h2,kk_6_3,kk_6_2,kk_6_1]) ).

thf(kk_6_4,axiom,
    ~ ( sP7
     => ~ sP38 ) ).

thf(36,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[kk_6_4,35,h1,h2]) ).

thf(0,theorem,
    ~ sP29,
    inference(contra,[status(thm),contra(discharge,[h0])],[36,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : PUZ081^1 : TPTP v8.1.0. Released v3.6.0.
% 0.07/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n027.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
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sun May 29 03:09:30 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 25.80/26.03  % SZS status Theorem
% 25.80/26.03  % Mode: mode461
% 25.80/26.03  % Inferences: 210
% 25.80/26.03  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------