## TPTP Problem File: SEV266^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV266^5 : 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_1038 [Bro09]

% Status   : Theorem
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :    1 (   0 unit;   0 type;   0 defn)
%            Number of atoms       :   34 (   1 equality;  33 variable)
%            Maximal formula depth :   12 (  12 average)
%            Number of connectives :   31 (   0   ~;   1   |;   5   &;  17   @)
%                                         (   1 <=>;   7  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    2 (   0   :;   0   =)
%            Number of variables   :   14 (   0 sgn;  10   !;   1   ?;   3   ^)
%                                         (  14   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_EQU_NAR

% Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
%            project in the Department of Mathematical Sciences at Carnegie
%          : May require description or choice.
%------------------------------------------------------------------------------
thf(cTHM4_pme,conjecture,
( ! [P: \$i > \$o,Q: \$i > \$o] :
( ! [X: \$i] :
( ( P @ X )
<=> ( Q @ X ) )
=> ( P = Q ) )
=> ! [T: ( \$i > \$o ) > \$o] :
( ( ! [S: ( \$i > \$o ) > \$o] :
( ! [Xx: \$i > \$o] :
( ( S @ Xx )
=> ( T @ Xx ) )
=> ( T
@ ^ [Xx: \$i] :
? [S0: \$i > \$o] :
( ( S @ S0 )
& ( S0 @ Xx ) ) ) )
& ! [P: \$i > \$o,Q: \$i > \$o] :
( ( ( T @ P )
& ( T @ Q ) )
=> ( T
@ ^ [Xx: \$i] :
( ( P @ Xx )
& ( Q @ Xx ) ) ) ) )
=> ! [U: \$i > \$o,V: \$i > \$o] :
( ( ( T @ U )
& ( T @ V ) )
=> ( T
@ ^ [Xz: \$i] :
( ( U @ Xz )
| ( V @ Xz ) ) ) ) ) )).

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