%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : DAT333^3 : TPTP v8.1.2. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n007.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 : Wed Aug 30 22:17:50 EDT 2023

% Result   : Theorem 0.20s 0.41s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   39
% Syntax   : Number of formulae    :   44 (  18 unt;  11 typ;  11 def)
%            Number of atoms       :   76 (  11 equ;   1 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  133 (  21   ~;   9   |;   2   &;  77   @)
%                                         (   9 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   3 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   22 (  22   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   32 (  29 usr;  29 con; 0-3 aty)
%            Number of variables   :   40 (  28   ^;  10   !;   2   ?;  40   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_mworld,type,
    mworld: $tType ).

thf(ty_mrel,type,
    mrel: mworld > mworld > $o ).

thf(ty_teach,type,
    teach: $i > $i > mworld > $o ).

thf(ty_john,type,
    john: $i ).

thf(ty_psych,type,
    psych: $i ).

thf(ty_eigen__3,type,
    eigen__3: mworld ).

thf(ty_mary,type,
    mary: $i ).

thf(ty_mactual,type,
    mactual: mworld ).

thf(ty_sue,type,
    sue: $i ).

thf(ty_cs,type,
    cs: $i ).

thf(ty_math,type,
    math: $i ).

thf(h0,assumption,
    ! [X1: mworld > $o,X2: mworld] :
      ( ( X1 @ X2 )
     => ( X1 @ ( eps__0 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(eigendef_eigen__3,definition,
    ( eigen__3
    = ( eps__0
      @ ^ [X1: mworld] :
          ~ ( ( mrel @ mactual @ X1 )
           => ( teach @ john @ math @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__3])]) ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: mworld] :
        ( ( mrel @ mactual @ X1 )
       => ~ ( ( teach @ john @ math @ X1 )
           => ( ~ ! [X2: $i] :
                    ~ ( teach @ X2 @ cs @ X1 )
             => ( ( teach @ mary @ psych @ X1 )
               => ~ ( teach @ sue @ psych @ X1 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: mworld] :
        ( ( mrel @ mactual @ X1 )
       => ( teach @ john @ math @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( teach @ john @ math @ eigen__3 )
     => ( ~ ! [X1: $i] :
              ~ ( teach @ X1 @ cs @ eigen__3 )
       => ( ( teach @ mary @ psych @ eigen__3 )
         => ~ ( teach @ sue @ psych @ eigen__3 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( mrel @ mactual @ eigen__3 )
     => ~ sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( teach @ john @ math @ eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: $i] :
        ~ ! [X2: mworld] :
            ( ( mrel @ mactual @ X2 )
           => ( teach @ john @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( mrel @ mactual @ eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( sP7
     => sP5 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(def_mlocal,definition,
    ( mlocal
    = ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ) ).

thf(def_mnot,definition,
    ( mnot
    = ( ^ [X1: mworld > $o,X2: mworld] : ( (~) @ ( X1 @ X2 ) ) ) ) ).

thf(def_mand,definition,
    ( mand
    = ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
          ( ( X1 @ X3 )
          & ( X2 @ X3 ) ) ) ) ).

thf(def_mor,definition,
    ( mor
    = ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
          ( ( X1 @ X3 )
          | ( X2 @ X3 ) ) ) ) ).

thf(def_mimplies,definition,
    ( mimplies
    = ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( X1 @ X3 )
          @ ( X2 @ X3 ) ) ) ) ).

thf(def_mequiv,definition,
    ( mequiv
    = ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
          ( ( X1 @ X3 )
        <=> ( X2 @ X3 ) ) ) ) ).

thf(def_mbox,definition,
    ( mbox
    = ( ^ [X1: mworld > $o,X2: mworld] :
        ! [X3: mworld] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( mrel @ X2 @ X3 )
          @ ( X1 @ X3 ) ) ) ) ).

thf(def_mdia,definition,
    ( mdia
    = ( ^ [X1: mworld > $o,X2: mworld] :
        ? [X3: mworld] :
          ( ( mrel @ X2 @ X3 )
          & ( X1 @ X3 ) ) ) ) ).

thf(def_mforall_di,definition,
    ( mforall_di
    = ( ^ [X1: $i > mworld > $o,X2: mworld] :
        ! [X3: $i] : ( X1 @ X3 @ X2 ) ) ) ).

thf(def_mexists_di,definition,
    ( mexists_di
    = ( ^ [X1: $i > mworld > $o,X2: mworld] :
        ? [X3: $i] : ( X1 @ X3 @ X2 ) ) ) ).

thf(query,conjecture,
    ~ sP6 ).

thf(h1,negated_conjecture,
    sP6,
    inference(assume_negation,[status(cth)],[query]) ).

thf(1,plain,
    ( sP3
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP4
    | ~ sP7
    | ~ sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP1
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( sP8
    | ~ sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( sP8
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( sP2
    | ~ sP8 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).

thf(7,plain,
    ( ~ sP6
    | ~ sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(db,axiom,
    sP1 ).

thf(8,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,h1,db]) ).

thf(9,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[8,h0]) ).

thf(0,theorem,
    ~ sP6,
    inference(contra,[status(thm),contra(discharge,[h1])],[8,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : DAT333^3 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34  % Computer : n007.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 : Thu Aug 24 14:11:25 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.20/0.41  % SZS status Theorem
% 0.20/0.41  % Mode: cade22grackle2xfee4
% 0.20/0.41  % Steps: 192
% 0.20/0.41  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------