## TPTP Problem File: SEV401^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV401^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory
% Problem  : TPS problem THM67
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0490 [Bro09]
%          : THM67 [TPS]

% Status   : Theorem
% Rating   : 0.08 v7.4.0, 0.00 v6.2.0, 0.33 v6.1.0, 0.17 v6.0.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% Syntax   : Number of formulae    :    4 (   0 unit;   3 type;   0 defn)
%            Number of atoms       :   30 (   0 equality;  20 variable)
%            Maximal formula depth :   10 (   5 average)
%            Number of connectives :   29 (   0   ~;   0   |;   2   &;  20   @)
%                                         (   1 <=>;   6  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3   :;   0   =)
%            Number of variables   :   10 (   0 sgn;  10   !;   0   ?;   0   ^)
%                                         (  10   :;   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(a_type,type,(
a: \$tType )).

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

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

thf(cTHM67_pme,conjecture,
( ( ! [S: a > \$o,T: a > \$o] :
( ! [Xx: a] :
( ( S @ Xx )
=> ( T @ Xx ) )
=> ! [Xx: a] :
( ( cF @ T @ Xx )
=> ( cF @ S @ Xx ) ) )
& ! [S: a > \$o,Xx: a] :
( ( S @ Xx )
=> ( cF @ ( cG @ S ) @ Xx ) )
& ! [S: a > \$o,Xx: a] :
( ( S @ Xx )
=> ( cG @ ( cF @ S ) @ Xx ) ) )
=> ! [S: a > \$o,Xx: a] :
( ( cF @ ( cG @ ( cF @ S ) ) @ Xx )
<=> ( cF @ S @ Xx ) ) )).

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