%------------------------------------------------------------------------------
% File     : PUZ047^5 : TPTP v8.2.0. Released v4.0.0.
% Domain   : Puzzles
% Problem  : TPS problem THM100A
% Version  : Especial.
% English  : A naive formalization of the problem of moving man wolf goat
%            cabbage from south to north side of river.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0543 [Bro09]
%          : tps_0544 [Bro09]
%          : tps_0545 [Bro09]
%          : tps_0427 [Bro09]
%          : THM100 [TPS]
%          : THM100A [TPS]
%          : THM100B [TPS]
%          : THM100-TPS2 [TPS]

% Status   : Theorem
% Rating   : 0.25 v8.2.0, 0.27 v8.1.0, 0.25 v7.4.0, 0.22 v7.3.0, 0.20 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.25 v6.4.0, 0.29 v6.3.0, 0.33 v6.2.0, 0.17 v6.1.0, 0.33 v6.0.0, 0.17 v5.5.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.1, 0.33 v4.0.0
% Syntax   : Number of formulae    :   11 (   0 unt;  10 typ;   0 def)
%            Number of atoms       :   30 (   0 equ;   0 cnn)
%            Maximal formula atoms :   30 (  30 avg)
%            Number of connectives :  193 (   0   ~;   0   |;  14   &; 164   @)
%                                         (   0 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (  23 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   8 usr;   3 con; 0-5 aty)
%            Number of variables   :   19 (   0   ^;  18   !;   1   ?;  19   :)
% SPC      : TH0_THM_NEQ_NAR

% Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
%            project in the Department of Mathematical Sciences at Carnegie
%            Mellon University. Distributed under the Creative Commons copyleft
%            license: http://creativecommons.org/licenses/by-sa/3.0/
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thf(a_type,type,
    a: $tType ).

thf(b_type,type,
    b: $tType ).

thf(cN,type,
    cN: a ).

thf(cP,type,
    cP: a > a > a > a > b > $o ).

thf(cD,type,
    cD: b > b ).

thf(cS,type,
    cS: a ).

thf(cG,type,
    cG: b > b ).

thf(cW,type,
    cW: b > b ).

thf(cL,type,
    cL: b > b ).

thf(cO,type,
    cO: b ).

thf(cTHM100A,conjecture,
    ( ( ( cP @ cS @ cS @ cS @ cS @ cO )
      & ! [T: b] :
          ( ( cP @ cS @ cN @ cS @ cN @ T )
         => ( cP @ cN @ cN @ cS @ cN @ ( cL @ T ) ) )
      & ! [T1: b] :
          ( ( cP @ cN @ cN @ cS @ cN @ T1 )
         => ( cP @ cS @ cN @ cS @ cN @ ( cL @ T1 ) ) )
      & ! [T2: b] :
          ( ( cP @ cS @ cS @ cN @ cS @ T2 )
         => ( cP @ cN @ cS @ cN @ cS @ ( cL @ T2 ) ) )
      & ! [T3: b] :
          ( ( cP @ cN @ cS @ cN @ cS @ T3 )
         => ( cP @ cS @ cS @ cN @ cS @ ( cL @ T3 ) ) )
      & ! [T4: b] :
          ( ( cP @ cS @ cS @ cS @ cN @ T4 )
         => ( cP @ cN @ cN @ cS @ cN @ ( cW @ T4 ) ) )
      & ! [T5: b] :
          ( ( cP @ cN @ cN @ cS @ cN @ T5 )
         => ( cP @ cS @ cS @ cS @ cN @ ( cW @ T5 ) ) )
      & ! [T6: b] :
          ( ( cP @ cS @ cS @ cN @ cS @ T6 )
         => ( cP @ cN @ cN @ cN @ cS @ ( cW @ T6 ) ) )
      & ! [T7: b] :
          ( ( cP @ cN @ cN @ cN @ cS @ T7 )
         => ( cP @ cS @ cS @ cN @ cS @ ( cW @ T7 ) ) )
      & ! [X: a,Y: a,U: b] :
          ( ( cP @ cS @ X @ cS @ Y @ U )
         => ( cP @ cN @ X @ cN @ Y @ ( cG @ U ) ) )
      & ! [X1: a,Y1: a,V: b] :
          ( ( cP @ cN @ X1 @ cN @ Y1 @ V )
         => ( cP @ cS @ X1 @ cS @ Y1 @ ( cG @ V ) ) )
      & ! [T8: b] :
          ( ( cP @ cS @ cN @ cS @ cS @ T8 )
         => ( cP @ cN @ cN @ cS @ cN @ ( cD @ T8 ) ) )
      & ! [T9: b] :
          ( ( cP @ cN @ cN @ cS @ cN @ T9 )
         => ( cP @ cS @ cN @ cS @ cS @ ( cD @ T9 ) ) )
      & ! [U1: b] :
          ( ( cP @ cS @ cS @ cN @ cS @ U1 )
         => ( cP @ cN @ cS @ cN @ cN @ ( cD @ U1 ) ) )
      & ! [V1: b] :
          ( ( cP @ cN @ cS @ cN @ cN @ V1 )
         => ( cP @ cS @ cS @ cN @ cS @ ( cD @ V1 ) ) ) )
   => ? [Z: b] : ( cP @ cN @ cN @ cN @ cN @ Z ) ) ).

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