## TPTP Problem File: SEV252^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV252^5 : 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_1051 [Bro09]

% Status   : Theorem
% Rating   : 0.67 v7.5.0, 0.58 v7.4.0, 0.56 v7.3.0, 0.60 v7.2.0, 0.62 v7.1.0, 0.57 v7.0.0, 0.62 v6.4.0, 0.71 v6.3.0, 0.83 v6.2.0, 0.67 v6.1.0, 0.83 v6.0.0, 0.67 v5.5.0, 0.60 v5.4.0, 0.50 v5.2.0, 0.75 v4.1.0, 1.00 v4.0.0
% Syntax   : Number of formulae    :    1 (   0 unit;   0 type;   0 defn)
%            Number of atoms       :   36 (   0 equality;  36 variable)
%            Maximal formula depth :   14 (  14 average)
%            Number of connectives :   35 (   0   ~;   0   |;   3   &;  22   @)
%                                         (   1 <=>;   9  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    2 (   0   :;   0   =)
%            Number of variables   :   15 (   0 sgn;  12   !;   2   ?;   1   ^)
%                                         (  15   :;   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
%------------------------------------------------------------------------------
thf(cTHM2A_EXPANDED_pme,conjecture,(
! [K: ( \$i > \$o ) > \$i > \$o] :
( ( ! [Xx: \$i > \$o,Xy: \$i > \$o] :
( ! [Xx0: \$i] :
( ( Xx @ Xx0 )
=> ( Xy @ Xx0 ) )
=> ! [Xx0: \$i] :
( ( K @ Xx @ Xx0 )
=> ( K @ Xy @ Xx0 ) ) )
& ! [Xx: \$i > \$o,Xy: \$i > \$o] :
( ! [Xx0: \$i] :
( ( Xx @ Xx0 )
=> ( Xy @ Xx0 ) )
=> ! [Xx0: \$i] :
( ( K @ Xx @ Xx0 )
=> ( K @ Xy @ Xx0 ) ) ) )
=> ! [Xx: \$i] :
( ( K
@ ^ [Xx0: \$i] :
? [S: \$i > \$o] :
( ! [Xx1: \$i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx )
<=> ? [S: \$i > \$o] :
( ! [Xx0: \$i] :
( ( S @ Xx0 )
=> ( K @ S @ Xx0 ) )
& ( S @ Xx ) ) ) ) )).

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