## TPTP Problem File: PUZ101^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : PUZ101^5 : TPTP v7.1.0. Bugfixed v5.2.0.
% Domain   : Puzzles
% Problem  : TPS problem from CHECKERBOARD-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0597 [Bro09]

% Status   : CounterSatisfiable
% Rating   : 0.33 v6.4.0, 0.67 v6.3.0, 0.33 v5.2.0
% Syntax   : Number of formulae    :   13 (   0 unit;   9 type;   3 defn)
%            Number of atoms       :  121 (  17 equality;  57 variable)
%            Maximal formula depth :   17 (   7 average)
%            Number of connectives :   84 (   1   ~;   3   |;  15   &;  62   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   27 (  27   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9   :;   0   =)
%            Number of variables   :   17 (   0 sgn;   5   !;   2   ?;  10   ^)
%                                         (  17   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_CSA_EQU_NAR

% Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
%            project in the Department of Mathematical Sciences at Carnegie
% Bugfixes : v5.2.0 - Added missing type declarations.
%------------------------------------------------------------------------------
thf(c1_type,type,(
c1: \$i )).

thf(c2_type,type,(
c2: \$i )).

thf(c3_type,type,(
c3: \$i )).

thf(c4_type,type,(
c4: \$i )).

thf(g_type,type,(
g: \$i > \$i > \$i )).

thf(s_type,type,(
s: \$i > \$i )).

thf(cCKB6_BLACK_type,type,(
cCKB6_BLACK: \$i > \$i > \$o )).

thf(cCKB6_H_type,type,(
cCKB6_H: \$i > \$i > \$i > \$i > \$o )).

thf(cCKB_XPL_type,type,(
cCKB_XPL: ( \$i > \$i > \$i > \$i > \$o ) > ( \$i > \$i > \$o ) > \$i > \$i > \$o )).

thf(cCKB6_BLACK_def,definition,
( cCKB6_BLACK
= ( ^ [Xu: \$i,Xv: \$i] :
! [Xw: \$i > \$i > \$o] :
( ( ( Xw @ c1 @ c1 )
& ! [Xj: \$i,Xk: \$i] :
( ( Xw @ Xj @ Xk )
=> ( ( Xw @ ( s @ ( s @ Xj ) ) @ Xk )
& ( Xw @ ( s @ Xj ) @ ( s @ Xk ) ) ) ) )
=> ( Xw @ Xu @ Xv ) ) ) )).

thf(cCKB6_H_def,definition,
( cCKB6_H
= ( ^ [Xx: \$i,Xy: \$i,Xu: \$i,Xv: \$i] :
( ( cCKB6_BLACK @ Xx @ Xy )
& ( ( ( ( g @ ( s @ ( s @ Xx ) ) @ ( s @ Xy ) )
= c1 )
& ( Xu
= ( s @ ( s @ ( s @ Xx ) ) ) )
& ( Xv
= ( s @ Xy ) ) )
| ( ( ( g @ ( s @ ( s @ Xx ) ) @ ( s @ Xy ) )
= c2 )
& ( Xu
= ( s @ ( s @ Xx ) ) )
& ( Xv
= ( s @ ( s @ Xy ) ) ) )
| ( ( ( g @ ( s @ ( s @ Xx ) ) @ ( s @ Xy ) )
= c3 )
& ( Xu
= ( s @ Xx ) )
& ( Xv
= ( s @ Xy ) ) )
| ( ( ( g @ ( s @ ( s @ Xx ) ) @ ( s @ Xy ) )
= c4 )
& ( Xu
= ( s @ ( s @ Xx ) ) )
& ( Xv = Xy ) ) ) ) ) )).

thf(cCKB_XPL_def,definition,
( cCKB_XPL
= ( ^ [Xh: \$i > \$i > \$i > \$i > \$o,Xk: \$i > \$i > \$o,Xm: \$i,Xn: \$i] :
( ( Xk @ Xm @ Xn )
& ! [Xx: \$i,Xy: \$i] :
( ( Xk @ Xx @ Xy )
=> ? [Xu: \$i,Xv: \$i] :
( ( Xh @ Xx @ Xy @ Xu @ Xv )
& ( Xk @ Xu @ Xv )
& ~ ( ( Xu = Xm )
& ( Xv = Xn ) ) ) ) ) ) )).

thf(cCKB6_L40000,conjecture,
( cCKB_XPL @ cCKB6_H @ cCKB6_BLACK @ c1 @ c1 )).

%------------------------------------------------------------------------------
```