## TPTP Problem File: SEV279^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV279^5 : 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_1050 [Bro09]

% Status   : Unknown
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :    5 (   0 unit;   4 type;   0 defn)
%            Number of atoms       :   36 (   2 equality;  30 variable)
%            Maximal formula depth :   15 (   5 average)
%            Number of connectives :   31 (   0   ~;   0   |;   6   &;  17   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   13 (  13   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4   :;   0   =)
%            Number of variables   :   14 (   0 sgn;   8   !;   5   ?;   1   ^)
%                                         (  14   :;   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(b_type,type,(
b: \$tType )).

thf(a_type,type,(
a: \$tType )).

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

thf(cW,type,(
cW: ( b > \$o ) > \$o )).

thf(cLEM562A_pme,conjecture,
( ( ! [U: ( b > \$o ) > \$o] :
( ( ? [Z: b > \$o] :
( U @ Z )
& ! [Xx: b > \$o] :
( ( U @ Xx )
=> ( cW @ Xx ) ) )
=> ( cW
@ ^ [Xx: b] :
! [S: b > \$o] :
( ( U @ S )
=> ( S @ Xx ) ) ) )
& ! [Xx: a] :
? [V: b > \$o] :
( ( cW @ V )
& ( Xx
= ( h @ V ) ) ) )
=> ? [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 ) ) ) ) )).

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