## TPTP Problem File: SEV223^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV223^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem X5204
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0535 [Bro09]
%          : X5204 [TPS]

% Status   : Theorem
% Rating   : 0.36 v7.5.0, 0.29 v7.4.0, 0.33 v7.2.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.43 v6.1.0, 0.29 v6.0.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v5.3.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% Syntax   : Number of formulae    :    5 (   0 unit;   4 type;   0 defn)
%            Number of atoms       :   21 (   4 equality;  13 variable)
%            Maximal formula depth :   13 (   5 average)
%            Number of connectives :   12 (   0   ~;   0   |;   5   &;   7   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4   :;   0   =)
%            Number of variables   :    8 (   0 sgn;   0   !;   5   ?;   3   ^)
%                                         (   8   :;   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(b_type,type,(
b: \$tType )).

thf(a_type,type,(
a: \$tType )).

thf(f,type,(
f: b > a )).

thf(w,type,(
w: ( b > \$o ) > \$o )).

thf(cX5204_pme,conjecture,
( ( ^ [Xz: a] :
? [Xt: b] :
( ? [S: b > \$o] :
( ( w @ S )
& ( S @ Xt ) )
& ( Xz
= ( f @ Xt ) ) ) )
= ( ^ [Xx: a] :
? [S: a > \$o] :
( ? [Xt: b > \$o] :
( ( w @ Xt )
& ( S
= ( ^ [Xz: a] :
? [Xt0: b] :
( ( Xt @ Xt0 )
& ( Xz
= ( f @ Xt0 ) ) ) ) ) )
& ( S @ Xx ) ) ) )).

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