## TPTP Problem File: PUZ095^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : PUZ095^5 : TPTP v7.2.0. Bugfixed v6.2.0.
% Domain   : Puzzles
% Problem  : TPS problem from CHECKERBOARD-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0580 [Bro09]

% Status   : CounterSatisfiable
% Rating   : 0.50 v7.2.0, 0.33 v6.4.0, 0.67 v6.3.0, 0.33 v6.2.0
% Syntax   : Number of formulae    :   11 (   0 unit;   6 type;   4 defn)
%            Number of atoms       :   72 (   8 equality;  50 variable)
%            Maximal formula depth :   17 (   8 average)
%            Number of connectives :   52 (   1   ~;   0   |;   9   &;  38   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   39 (  39   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6   :;   0   =)
%            Number of variables   :   24 (   0 sgn;  11   !;   5   ?;   8   ^)
%                                         (  24   :;   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.
%          : v6.2.0 - Reordered definitions.
%------------------------------------------------------------------------------
thf(c1_type,type,(
c1: \$i )).

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

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

thf(cCKB_INF_type,type,(
cCKB_INF: ( \$i > \$i > \$o ) > \$o )).

thf(cCKB_INJ_type,type,(
cCKB_INJ: ( \$i > \$i > \$i > \$i > \$o ) > \$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(cCKB_INJ_def,definition,
( cCKB_INJ
= ( ^ [Xh: \$i > \$i > \$i > \$i > \$o] :
! [Xx1: \$i,Xy1: \$i,Xx2: \$i,Xy2: \$i,Xu: \$i,Xv: \$i] :
( ( ( Xh @ Xx1 @ Xy1 @ Xu @ Xv )
& ( Xh @ Xx2 @ Xy2 @ Xu @ Xv ) )
=> ( ( Xx1 = Xx2 )
& ( Xy1 = Xy2 ) ) ) ) )).

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(cCKB_INF_def,definition,
( cCKB_INF
= ( ^ [Xk: \$i > \$i > \$o] :
? [Xh: \$i > \$i > \$i > \$i > \$o,Xm: \$i,Xn: \$i] :
( ( cCKB_INJ @ Xh )
& ( cCKB_XPL @ Xh @ Xk @ Xm @ Xn ) ) ) )).

thf(cCKB6_L50000,conjecture,
( cCKB_INF @ cCKB6_BLACK )).

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