## TPTP Problem File: SEV281^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV281^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem from WELL-ORD-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1151 [Bro09]

% Status   : Unknown
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :    3 (   0 unit;   2 type;   0 defn)
%            Number of atoms       :   68 (   2 equality;  56 variable)
%            Maximal formula depth :   16 (   7 average)
%            Number of connectives :   63 (   0   ~;   2   |;  12   &;  37   @)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   2   :;   0   =)
%            Number of variables   :   21 (   0 sgn;  17   !;   4   ?;   0   ^)
%                                         (  21   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_UNK_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(a_type,type,(
a: \$tType )).

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

thf(cTHM548_pme,conjecture,
( ( ? [W: a > a > \$o] :
! [X: a > \$o] :
( ? [Xz: a] :
( X @ Xz )
=> ? [Xz: a] :
( ( X @ Xz )
& ! [Xx: a] :
( ( X @ Xx )
=> ( W @ Xz @ Xx ) )
& ! [Xy: a] :
( ( ( X @ Xy )
& ! [Xx: a] :
( ( X @ Xx )
=> ( W @ Xy @ Xx ) ) )
=> ( Xy = Xz ) ) ) )
& ! [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 ) ) )
=> ? [S: a > \$o] :
( ! [Xx: a,Xy: a] :
( ( ( S @ Xx )
& ( S @ Xy ) )
=> ( ( cR @ Xx @ Xy )
| ( cR @ Xy @ Xx ) ) )
& ! [T: a > \$o] :
( ( ! [Xx: a,Xy: a] :
( ( ( T @ Xx )
& ( T @ Xy ) )
=> ( ( cR @ Xx @ Xy )
| ( cR @ Xy @ Xx ) ) )
& ! [Xx: a] :
( ( S @ Xx )
=> ( T @ Xx ) ) )
=> ! [Xx: a] :
( ( T @ Xx )
=> ( S @ Xx ) ) ) ) )).

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