## TPTP Problem File: PUZ127^5.p

View Solutions - Solve Problem

%------------------------------------------------------------------------------
% File     : PUZ127^5 : TPTP v7.2.0. Released v4.0.0.
% Domain   : Puzzles
% Problem  : TPS problem from CHECKERBOARD-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1182 [Bro09]

% Status   : Theorem
% Rating   : 0.67 v7.2.0, 0.62 v7.1.0, 0.75 v7.0.0, 0.71 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 0.71 v5.5.0, 0.67 v5.4.0, 1.00 v4.0.0
% Syntax   : Number of formulae    :    9 (   0 unit;   8 type;   0 defn)
%            Number of atoms       :  122 (  25 equality;  30 variable)
%            Maximal formula depth :   22 (   5 average)
%            Number of connectives :   77 (   6   ~;   5   |;  16   &;  47   @)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   8   :;   0   =)
%            Number of variables   :   11 (   0 sgn;  11   !;   0   ?;   0   ^)
%                                         (  11   :;   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
%------------------------------------------------------------------------------
thf(c5,type,(
c5: \$i )).

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

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

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

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

thf(c1,type,(
c1: \$i )).

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

thf(c8,type,(
c8: \$i )).

thf(cTOUGHNUT2,conjecture,(
~ ( ( ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ c8 ) ) ) ) ) ) ) )
= c8 )
& ! [Xx: \$i] :
( ( s @ ( s @ ( s @ ( s @ Xx ) ) ) )
!= Xx )
& ! [Xx: \$i,Xy: \$i] :
( ( ( g @ Xx @ Xy )
= c5 )
<=> ( ( ( Xx = c8 )
& ( Xy = c8 ) )
| ( ( Xx = c1 )
& ( Xy = c1 ) ) ) )
& ! [Xx: \$i,Xy: \$i] :
( ( ( g @ Xx @ Xy )
= c1 )
<=> ( ( g @ ( s @ Xx ) @ Xy )
= c3 ) )
& ! [Xx: \$i,Xy: \$i] :
( ( ( g @ Xx @ Xy )
= c2 )
<=> ( ( g @ Xx @ ( s @ Xy ) )
= c4 ) )
& ! [Xx: \$i,Xy: \$i] :
( ( ( g @ c1 @ Xy )
!= c3 )
& ( ( g @ c8 @ Xy )
!= c1 )
& ( ( g @ Xx @ c1 )
!= c4 )
& ( ( g @ Xx @ c8 )
!= c2 ) )
& ( c1
= ( s @ c8 ) )
& ( c2
= ( s @ c1 ) )
& ( c3
= ( s @ c2 ) )
& ( c4
= ( s @ c3 ) )
& ( c5
= ( s @ c4 ) )
& ! [Xx: \$i,Xy: \$i] :
( ( ( g @ Xx @ Xy )
= c1 )
| ( ( g @ Xx @ Xy )
= c2 )
| ( ( g @ Xx @ Xy )
= c3 )
| ( ( g @ Xx @ Xy )
= c4 )
| ( ( g @ Xx @ Xy )
= c5 ) ) ) )).

%------------------------------------------------------------------------------