## TPTP Problem File: SEV391^5.p

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%------------------------------------------------------------------------------
% File     : SEV391^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory
% Problem  : TPS problem THM87
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0205 [Bro09]
%          : THM87 [TPS]

% Status   : Theorem
% Rating   : 0.17 v7.5.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.0.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    5 (   0 unit;   4 type;   0 defn)
%            Number of atoms       :   14 (   0 equality;   8 variable)
%            Maximal formula depth :    9 (   4 average)
%            Number of connectives :   13 (   0   ~;   1   |;   0   &;  11   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4   :;   0   =)
%            Number of variables   :    3 (   0 sgn;   1   !;   2   ?;   0   ^)
%                                         (   3   :;   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(cP,type,(
cP: \$i > \$i > \$i > \$o )).

thf(k,type,(
k: \$i > \$i )).

thf(h,type,(
h: \$i > \$i )).

thf(a,type,(
a: \$i )).

thf(cTHM87_pme,conjecture,(
? [Xv: \$i] :
! [Xj: \$i] :
? [Xq: \$i] :
( ( ( cP @ a @ ( h @ Xj ) @ Xj )
| ( cP @ Xv @ ( k @ Xj ) @ Xj ) )
=> ( cP @ Xv @ Xq @ Xj ) ) )).

%------------------------------------------------------------------------------