## TPTP Problem File: SEV186^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV186^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem THM565
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0482 [Bro09]
%          : THM565 [TPS]

% Status   : Theorem
% Rating   : 0.08 v7.4.0, 0.00 v6.2.0, 0.17 v6.0.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   28 (   0 equality;  28 variable)
%            Maximal formula depth :   13 (   8 average)
%            Number of connectives :   27 (   0   ~;   0   |;   2   &;  15   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   13 (  13   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :   13 (   0 sgn;  13   !;   0   ?;   0   ^)
%                                         (  13   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_NEQ_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(b_type,type,(
b: \$tType )).

thf(cTHM565_pme,conjecture,(
! [P: ( b > \$o ) > ( b > \$o ) > \$o,S: ( b > \$o ) > \$o] :
( ! [Xx: b > \$o] :
( ( S @ Xx )
=> ! [X: b > \$o,Y: b > \$o] :
( ( ! [Xx0: b] :
( ( X @ Xx0 )
=> ( Xx @ Xx0 ) )
& ( P @ X @ Y ) )
=> ! [Xx0: b] :
( ( Y @ Xx0 )
=> ( Xx @ Xx0 ) ) ) )
=> ! [X: b > \$o,Y: b > \$o] :
( ( ! [Xx: b] :
( ( X @ Xx )
=> ! [S0: b > \$o] :
( ( S @ S0 )
=> ( S0 @ Xx ) ) )
& ( P @ X @ Y ) )
=> ! [Xx: b] :
( ( Y @ Xx )
=> ! [S0: b > \$o] :
( ( S @ S0 )
=> ( S0 @ Xx ) ) ) ) ) )).

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