## TPTP Problem File: SEV232^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV232^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem X6007
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0359 [Bro09]
%          : X6007 [TPS]

% Status   : Theorem
% Rating   : 0.09 v7.5.0, 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 v4.1.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    3 (   0 unit;   2 type;   0 defn)
%            Number of atoms       :   19 (   1 equality;  14 variable)
%            Maximal formula depth :   10 (   6 average)
%            Number of connectives :   16 (   0   ~;   0   |;   2   &;  10   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   21 (  21   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   2   :;   0   =)
%            Number of variables   :    6 (   0 sgn;   4   !;   0   ?;   2   ^)
%                                         (   6   :;   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(cS,type,(
cS: ( ( \$i > \$o ) > \$o ) > ( \$i > \$o ) > \$o )).

thf(c0,type,(
c0: ( \$i > \$o ) > \$o )).

thf(cX6007_pme,conjecture,
( ( ^ [N: ( \$i > \$o ) > \$o] :
! [P: ( ( \$i > \$o ) > \$o ) > \$o] :
( ( ( P @ c0 )
& ! [X: ( \$i > \$o ) > \$o] :
( ( P @ X )
=> ( P @ ( cS @ X ) ) ) )
=> ( P @ N ) ) )
= ( ^ [Xx: ( \$i > \$o ) > \$o] :
! [S0: ( ( \$i > \$o ) > \$o ) > \$o] :
( ( ( S0 @ c0 )
& ! [X: ( \$i > \$o ) > \$o] :
( ( S0 @ X )
=> ( S0 @ ( cS @ X ) ) ) )
=> ( S0 @ Xx ) ) ) )).

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