## TPTP Problem File: SEU969^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEU969^5 : TPTP v8.1.2. 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   : 0.62 v8.1.0, 0.55 v7.5.0, 0.29 v7.4.0, 0.56 v7.3.0, 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 (   2 unt;   4 typ;   2 def)
%            Number of atoms       :    7 (   2 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   32 (   0   ~;   0   |;   4   &;  23   @)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   4 usr;   1 con; 0-2 aty)
%            Number of variables   :   10 (   3   ^   7   !;   0   ?;  10   :)
% 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 ) ) ) ).

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