## TPTP Problem File: SEV259^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV259^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem CLOSURE-THM0
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0339 [Bro09]
%          : CLOSURE-THM0 [TPS]

% Status   : Theorem
% Rating   : 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 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 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   48 (   5 equality;  41 variable)
%            Maximal formula depth :   16 (   9 average)
%            Number of connectives :   39 (   2   ~;   0   |;   9   &;  18   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   15 (  15   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   1   :;   0   =)
%            Number of variables   :   20 (   2 sgn;  14   !;   1   ?;   5   ^)
%                                         (  20   :;   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
%            Mellon University. Distributed under the Creative Commons copyleft
%            license: http://creativecommons.org/licenses/by-sa/3.0/
%          : Polymorphic definitions expanded.
%------------------------------------------------------------------------------
thf(b_type,type,(
b: \$tType )).

thf(cCLOSURE_THM0_pme,conjecture,(
! [S: ( b > \$o ) > \$o] :
( ( ! [R: b > \$o] :
( ( R
= ( ^ [Xx: b] : \$false ) )
=> ( S @ R ) )
& ! [R: b > \$o] :
( ( R
= ( ^ [Xx: b] : ~ ( \$false ) ) )
=> ( S @ R ) )
& ! [K: ( b > \$o ) > \$o,R: b > \$o] :
( ( ! [Xx: b > \$o] :
( ( K @ Xx )
=> ( S @ Xx ) )
& ( R
= ( ^ [Xx: b] :
? [S0: b > \$o] :
( ( K @ S0 )
& ( S0 @ Xx ) ) ) ) )
=> ( S @ R ) )
& ! [Y: b > \$o,Z: b > \$o,S0: b > \$o] :
( ( ( S @ Y )
& ( S @ Z )
& ( S0
= ( ^ [Xx: b] :
( ( Y @ Xx )
& ( Z @ Xx ) ) ) ) )
=> ( S @ S0 ) ) )
=> ! [W: b > \$o,Xx: b] :
( ( W @ Xx )
=> ! [S0: b > \$o] :
( ( ! [Xx0: b] :
( ( W @ Xx0 )
=> ( S0 @ Xx0 ) )
& ! [R: b > \$o] :
( ( R
= ( ^ [Xx0: b] :
~ ( S0 @ Xx0 ) ) )
=> ( S @ R ) ) )
=> ( S0 @ Xx ) ) ) ) )).

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