## TPTP Problem File: SEV231^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV231^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem X5201
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0343 [Bro09]
%          : X5201 [TPS]

% Status   : Theorem
% Rating   : 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 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    :    4 (   0 unit;   3 type;   0 defn)
%            Number of atoms       :   13 (   3 equality;   6 variable)
%            Maximal formula depth :    7 (   4 average)
%            Number of connectives :    6 (   0   ~;   1   |;   1   &;   3   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3   :;   0   =)
%            Number of variables   :    3 (   0 sgn;   1   !;   0   ?;   2   ^)
%                                         (   3   :;   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(y,type,(
y: a > \$o )).

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

thf(cX5201_pme,conjecture,
( ( ^ [Xx0: a] :
( ( x @ Xx0 )
& ( y @ Xx0 ) ) )
= ( ^ [Xx0: a] :
! [S: a > \$o] :
( ( ( S = x )
| ( S = y ) )
=> ( S @ Xx0 ) ) ) )).

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