## TPTP Problem File: SEV242^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV242^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem from SETS-OF-SETS-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0919 [Bro09]

% Status   : Theorem
% Rating   : 0.27 v7.5.0, 0.29 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.80 v4.1.0, 1.00 v4.0.1, 0.67 v4.0.0
% Syntax   : Number of formulae    :    1 (   0 unit;   0 type;   0 defn)
%            Number of atoms       :   21 (   3 equality;  18 variable)
%            Maximal formula depth :   12 (  12 average)
%            Number of connectives :   14 (   0   ~;   2   |;   1   &;   7   @)
%                                         (   1 <=>;   3  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    2 (   0   :;   0   =)
%            Number of variables   :    9 (   0 sgn;   6   !;   1   ?;   2   ^)
%                                         (   9   :;   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
%------------------------------------------------------------------------------
thf(cTHM4A_pme,conjecture,
( ! [P: \$i > \$o,Q: \$i > \$o] :
( ! [X: \$i] :
( ( P @ X )
<=> ( Q @ X ) )
=> ( P = Q ) )
=> ! [T: ( \$i > \$o ) > \$o,U: \$i > \$o,V: \$i > \$o] :
( ( T
@ ^ [Xx: \$i] :
? [S: \$i > \$o] :
( ( ( S = U )
| ( S = V ) )
& ( S @ Xx ) ) )
=> ( T
@ ^ [Xz: \$i] :
( ( U @ Xz )
| ( V @ Xz ) ) ) ) )).

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