## TPTP Problem File: SEV067^5.p

View Solutions - Solve Problem

%------------------------------------------------------------------------------
% File     : SEV067^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem THM553
% Version  : Especial.
% English  : Downward closed subsets of a linear order are comparable.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0441 [Bro09]
%          : THM553 [TPS]

% Status   : Theorem
% Rating   : 0.09 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% Syntax   : Number of formulae    :    5 (   0 unit;   4 type;   0 defn)
%            Number of atoms       :   49 (   1 equality;  30 variable)
%            Maximal formula depth :   13 (   5 average)
%            Number of connectives :   46 (   0   ~;   2   |;   9   &;  28   @)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4   :;   0   =)
%            Number of variables   :   14 (   0 sgn;  14   !;   0   ?;   0   ^)
%                                         (  14   :;   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
%          : Polymorphic definitions expanded.
%------------------------------------------------------------------------------
thf(a_type,type,(
a: \$tType )).

thf(cS,type,(
cS: a > \$o )).

thf(cT,type,(
cT: a > \$o )).

thf(cR,type,(
cR: a > a > \$o )).

thf(cTHM553_pme,conjecture,
( ( ! [Xx: a,Xy: a,Xz: a] :
( ( ( cR @ Xx @ Xy )
& ( cR @ Xy @ Xz ) )
=> ( cR @ Xx @ Xz ) )
& ! [Xx: a] :
( cR @ Xx @ Xx )
& ! [Xx: a,Xy: a] :
( ( ( cR @ Xx @ Xy )
& ( cR @ Xy @ Xx ) )
=> ( Xx = Xy ) )
& ! [Xx: a,Xy: a] :
( ( cR @ Xx @ Xy )
| ( cR @ Xy @ Xx ) )
& ! [Xu: a,Xv: a] :
( ( ( cR @ Xu @ Xv )
& ( cS @ Xv ) )
=> ( cS @ Xu ) )
& ! [Xu: a,Xv: a] :
( ( ( cR @ Xu @ Xv )
& ( cT @ Xv ) )
=> ( cT @ Xu ) ) )
=> ( ! [Xx: a] :
( ( cS @ Xx )
=> ( cT @ Xx ) )
| ! [Xx: a] :
( ( cT @ Xx )
=> ( cS @ Xx ) ) ) )).

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