## TPTP Problem File: SEV278^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV278^5 : 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_0982 [Bro09]

% Status   : Unknown
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   27 (   1 equality;  26 variable)
%            Maximal formula depth :   15 (   8 average)
%            Number of connectives :   24 (   0   ~;   0   |;   3   &;  15   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :   11 (   0 sgn;   6   !;   5   ?;   0   ^)
%                                         (  11   :;   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(cTHM562_pme,conjecture,
( ! [Xg: ( ( a > \$o ) > a ) > a > \$o] :
( ! [Xh: ( a > \$o ) > a] :
? [Xu: a] :
( Xg @ Xh @ Xu )
=> ? [Xf: ( a > \$o ) > a] :
( Xg @ Xf @ ( Xf @ ( Xg @ Xf ) ) ) )
=> ? [R: a > a > \$o] :
! [X: a > \$o] :
( ? [Xz: a] :
( X @ Xz )
=> ? [Xz: a] :
( ( X @ Xz )
& ! [Xx: a] :
( ( X @ Xx )
=> ( R @ Xz @ Xx ) )
& ! [Xy: a] :
( ( ( X @ Xy )
& ! [Xx: a] :
( ( X @ Xx )
=> ( R @ Xy @ Xx ) ) )
=> ( Xy = Xz ) ) ) ) )).

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