## TPTP Problem File: SEV391^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV391^5 : TPTP v8.0.0. 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 unt;   4 typ;   0 def)
%            Number of atoms       :    3 (   0 equ;   0 cnn)
%            Maximal formula atoms :    3 (   3 avg)
%            Number of connectives :   13 (   0   ~;   1   |;   0   &;  11   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   4 usr;   1 con; 0-3 aty)
%            Number of variables   :    3 (   0   ^   1   !;   2   ?;   3   :)
% 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 ) ) ).

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