## TPTP Problem File: SEV271^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV271^5 : 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_1212 [Bro09]

% Status   : Unknown
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :    3 (   0 unit;   2 type;   0 defn)
%            Number of atoms       :  109 (  13 equality;  92 variable)
%            Maximal formula depth :   21 (   8 average)
%            Number of connectives :   86 (   4   ~;   0   |;  21   &;  40   @)
%                                         (   1 <=>;  20  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   32 (  32   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   2   :;   0   =)
%            Number of variables   :   44 (   4 sgn;  29   !;   4   ?;  11   ^)
%                                         (  44   :;   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
%------------------------------------------------------------------------------
thf(b_type,type,(
b: \$tType )).

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

thf(cCLOSURE_THM2_pme,conjecture,(
! [S: ( b > \$o ) > \$o,T: ( a > \$o ) > \$o] :
( ( ! [R: a > \$o] :
( ( R
= ( ^ [Xx: a] : \$false ) )
=> ( T @ R ) )
& ! [R: a > \$o] :
( ( R
= ( ^ [Xx: a] : ~ ( \$false ) ) )
=> ( T @ R ) )
& ! [K: ( a > \$o ) > \$o,R: a > \$o] :
( ( ! [Xx: a > \$o] :
( ( K @ Xx )
=> ( T @ Xx ) )
& ( R
= ( ^ [Xx: a] :
? [S0: a > \$o] :
( ( K @ S0 )
& ( S0 @ Xx ) ) ) ) )
=> ( T @ R ) )
& ! [Y: a > \$o,Z: a > \$o,S0: a > \$o] :
( ( ( T @ Y )
& ( T @ Z )
& ( S0
= ( ^ [Xx: a] :
( ( Y @ Xx )
& ( Z @ Xx ) ) ) ) )
=> ( T @ S0 ) )
& ! [R: b > \$o] :
( ( R
= ( ^ [Xx: b] : \$false ) )
=> ( S @ R ) )
& ! [R: b > \$o] :
( ( R
= ( ^ [Xx: b] : ~ ( \$false ) ) )
=> ( S @ R ) )
& ! [K: ( b > \$o ) > \$o,R: b > \$o] :
( ( ! [Xx: b > \$o] :
( ( K @ Xx )
=> ( S @ Xx ) )
& ( R
= ( ^ [Xx: b] :
? [S0: b > \$o] :
( ( K @ S0 )
& ( S0 @ Xx ) ) ) ) )
=> ( S @ R ) )
& ! [Y: b > \$o,Z: b > \$o,S0: b > \$o] :
( ( ( S @ Y )
& ( S @ Z )
& ( S0
= ( ^ [Xx: b] :
( ( Y @ Xx )
& ( Z @ Xx ) ) ) ) )
=> ( S @ S0 ) ) )
=> ! [F: b > a] :
( ! [X: a > \$o] :
( ( T @ X )
=> ! [Y: b > \$o] :
( ( Y
= ( ^ [Xb: b] :
( X @ ( F @ Xb ) ) ) )
=> ( S @ Y ) ) )
<=> ! [X: b > \$o,Xx: a] :
( ? [Xt: b] :
( ! [S0: b > \$o] :
( ( ! [Xx0: b] :
( ( X @ Xx0 )
=> ( S0 @ Xx0 ) )
& ! [R: b > \$o] :
( ( R
= ( ^ [Xx0: b] :
~ ( S0 @ Xx0 ) ) )
=> ( S @ R ) ) )
=> ( S0 @ Xt ) )
& ( Xx
= ( F @ Xt ) ) )
=> ! [S0: a > \$o] :
( ( ! [Xx0: a] :
( ? [Xt: b] :
( ( X @ Xt )
& ( Xx0
= ( F @ Xt ) ) )
=> ( S0 @ Xx0 ) )
& ! [R: a > \$o] :
( ( R
= ( ^ [Xx0: a] :
~ ( S0 @ Xx0 ) ) )
=> ( T @ R ) ) )
=> ( S0 @ Xx ) ) ) ) ) )).

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