## TPTP Problem File: SEU969^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEU969^5 : TPTP v7.2.0. Bugfixed v5.2.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem from CHECKERBOARD-RELNS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0682 [Bro09]

% Status   : Theorem
% Rating   : 0.67 v7.2.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.57 v5.5.0, 0.67 v5.4.0, 0.80 v5.2.0
% Syntax   : Number of formulae    :    7 (   0 unit;   4 type;   2 defn)
%            Number of atoms       :   39 (   2 equality;  24 variable)
%            Maximal formula depth :   15 (   6 average)
%            Number of connectives :   32 (   0   ~;   0   |;   4   &;  23   @)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4   :;   0   =)
%            Number of variables   :   10 (   0 sgn;   7   !;   0   ?;   3   ^)
%                                         (  10   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_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(s_type,type,(
s: \$i > \$i )).

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

thf(cCKB6_NUM_type,type,(
cCKB6_NUM: \$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_NUM_def,definition,
( cCKB6_NUM
= ( ^ [Xx: \$i] :
! [Xp: \$i > \$o] :
( ( ( Xp @ c1 )
& ! [Xw: \$i] :
( ( Xp @ Xw )
=> ( Xp @ ( s @ Xw ) ) ) )
=> ( Xp @ Xx ) ) ) )).

thf(cCKB6_L6000_pme,conjecture,(
! [Xx: \$i,Xy: \$i] :
( ( cCKB6_BLACK @ Xx @ Xy )
=> ( ( cCKB6_NUM @ Xx )
& ( cCKB6_NUM @ Xy ) ) ) )).

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