## TPTP Problem File: SEV221^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV221^5 : TPTP v8.0.0. Released v4.0.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem THM61
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0386 [Bro09]
%          : THM61 [TPS]

% Status   : Theorem
% Rating   : 0.36 v7.5.0, 0.29 v7.4.0, 0.33 v7.2.0, 0.25 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 v6.1.0, 0.14 v5.5.0, 0.33 v5.4.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% Syntax   : Number of formulae    :    4 (   0 unt;   3 typ;   0 def)
%            Number of atoms       :    5 (   1 equ;   0 cnn)
%            Maximal formula atoms :    4 (   5 avg)
%            Number of connectives :   13 (   0   ~;   0   |;   5   &;   7   @)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   8 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   2 usr;   0 con; 1-2 aty)
%            Number of variables   :    5 (   1   ^   1   !;   3   ?;   5   :)
% 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(cZ,type,
cZ: a > \$o ).

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

thf(cTHM61_pme,conjecture,
! [Xx: a] :
( ( ? [S: a > \$o] :
( ( cW @ S )
& ( S @ Xx ) )
& ( cZ @ Xx ) )
<=> ? [S: a > \$o] :
( ? [Xt: a > \$o] :
( ( cW @ Xt )
& ( S
= ( ^ [Xx0: a] :
( ( cZ @ Xx0 )
& ( Xt @ Xx0 ) ) ) ) )
& ( S @ Xx ) ) ) ).

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