## TPTP Problem File: SEV404^5.p

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```%------------------------------------------------------------------------------
% File     : SEV404^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory
% Problem  : TPS problem THM595
% Version  : Especial.
% English  : Existence of a stream of P values.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0550 [Bro09]
%          : THM595 [TPS]

% Status   : Theorem
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :    6 (   0 unit;   5 type;   0 defn)
%            Number of atoms       :   24 (   0 equality;  18 variable)
%            Maximal formula depth :   11 (   4 average)
%            Number of connectives :   23 (   0   ~;   0   |;   3   &;  14   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5   :;   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(b_type,type,(
b: \$tType )).

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

thf(cRST,type,(
cRST: b > b )).

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

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

thf(cTHM595_pme,conjecture,(
? [Xv: b > \$o] :
( ! [Xx: b] :
( ( Xv @ Xx )
=> ( cP @ ( cFST @ Xx ) ) )
& ! [Xx: b] :
( ( Xv @ Xx )
=> ( Xv @ ( cRST @ Xx ) ) )
& ! [Xu: b > \$o] :
( ( ! [Xx: b] :
( ( Xu @ Xx )
=> ( cP @ ( cFST @ Xx ) ) )
& ! [Xx: b] :
( ( Xu @ Xx )
=> ( Xu @ ( cRST @ Xx ) ) ) )
=> ! [Xx: b] :
( ( Xu @ Xx )
=> ( Xv @ Xx ) ) ) ) )).

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