## TPTP Problem File: SEV400^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV400^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory
% Problem  : TPS problem THM590
% Version  : Especial.
% English  : A simple theorem about existence of intersection.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0451 [Bro09]
%          : THM590 [TPS]

% Status   : Theorem
% Rating   : 0.75 v7.4.0, 0.67 v7.3.0, 0.70 v7.2.0, 0.62 v7.1.0, 0.57 v7.0.0, 0.75 v6.4.0, 0.71 v6.3.0, 0.67 v5.5.0, 0.80 v5.4.0, 0.75 v4.1.0, 0.67 v4.0.0
% Syntax   : Number of formulae    :    3 (   0 unit;   2 type;   0 defn)
%            Number of atoms       :   20 (   0 equality;  16 variable)
%            Maximal formula depth :   10 (   5 average)
%            Number of connectives :   19 (   0   ~;   0   |;   3   &;  10   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   2   :;   0   =)
%            Number of variables   :    7 (   0 sgn;   6   !;   1   ?;   0   ^)
%                                         (   7   :;   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(cQ,type,(
cQ: \$i > \$o )).

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

thf(cTHM590_pme,conjecture,(
? [S: \$i > \$o] :
( ! [Xx: \$i] :
( ( S @ Xx )
=> ( cP @ Xx ) )
& ! [Xx: \$i] :
( ( S @ Xx )
=> ( cQ @ Xx ) )
& ! [R: \$i > \$o] :
( ( ! [Xx: \$i] :
( ( R @ Xx )
=> ( cP @ Xx ) )
& ! [Xx: \$i] :
( ( R @ Xx )
=> ( cQ @ Xx ) ) )
=> ! [Xx: \$i] :
( ( R @ Xx )
=> ( S @ Xx ) ) ) ) )).

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