## TPTP Problem File: SEV270^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV270^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem from TOPOLOGY-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1129 [Bro09]

% Status   : Unknown
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :    3 (   0 unit;   2 type;   0 defn)
%            Number of atoms       :   53 (   1 equality;  44 variable)
%            Maximal formula depth :   17 (   8 average)
%            Number of connectives :   51 (   1   ~;   2   |;  10   &;  26   @)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   25 (  25   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   2   :;   0   =)
%            Number of variables   :   23 (   1 sgn;  15   !;   5   ?;   3   ^)
%                                         (  23   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_UNK_EQU_NAR

% Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
%            project in the Department of Mathematical Sciences at Carnegie
%            Mellon University. Distributed under the Creative Commons copyleft
%------------------------------------------------------------------------------
thf(cL,type,(
cL: ( \$i > \$o ) > \$o )).

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

thf(cTHM628_pme,conjecture,
( ( ! [C: ( \$i > \$o ) > \$o] :
( ( ! [Xx: \$i > \$o] :
( ( C @ Xx )
=> ( cG @ Xx ) )
& ! [Xx: \$i] :
? [Y: \$i > \$o] :
( ( C @ Y )
& ( Y @ Xx ) ) )
=> ? [D: ( \$i > \$o ) > \$o] :
( ! [Xw: ( ( \$i > \$o ) > \$o ) > \$o] :
( ( ( Xw
@ ^ [Xx: \$i > \$o] : \$false )
& ! [Xr: ( \$i > \$o ) > \$o,Xx: \$i > \$o] :
( ( Xw @ Xr )
=> ( Xw
@ ^ [Xt: \$i > \$o] :
( ( Xr @ Xt )
| ( Xt = Xx ) ) ) ) )
=> ( Xw @ D ) )
& ! [Xx: \$i > \$o] :
( ( D @ Xx )
=> ( C @ Xx ) )
& ! [Xx: \$i] :
? [Y: \$i > \$o] :
( ( D @ Y )
& ( Y @ Xx ) ) ) )
& ! [X: \$i > \$o,Y: \$i > \$o] :
( ( ( cL @ X )
& ( cL @ Y ) )
=> ( ! [Xx: \$i] :
( ( X @ Xx )
=> ( Y @ Xx ) )
| ! [Xx: \$i] :
( ( Y @ Xx )
=> ( X @ Xx ) ) ) )
& ! [Y: \$i > \$o] :
( ( cL @ Y )
=> ? [Xx: \$i] :
( Y @ Xx ) )
& ! [Y: \$i > \$o] :
( ( cL @ Y )
=> ( cG
@ ^ [Xx: \$i] :
~ ( Y @ Xx ) ) ) )
=> ? [Xa: \$i] :
! [Y: \$i > \$o] :
( ( cL @ Y )
=> ( Y @ Xa ) ) )).

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