## TPTP Problem File: SEV224^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV224^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem from FUNS-AND-SETS-OF-SETS-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0876 [Bro09]

% Status   : Theorem
% Rating   : 0.91 v7.5.0, 0.86 v7.4.0, 0.56 v7.2.0, 0.62 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.40 v6.2.0, 0.43 v5.5.0, 0.67 v5.4.0, 0.80 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0
% Syntax   : Number of formulae    :    3 (   0 unit;   2 type;   0 defn)
%            Number of atoms       :   16 (   2 equality;  14 variable)
%            Maximal formula depth :   14 (   6 average)
%            Number of connectives :   11 (   0   ~;   0   |;   1   &;   7   @)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   2   :;   0   =)
%            Number of variables   :    8 (   0 sgn;   5   !;   2   ?;   1   ^)
%                                         (   8   :;   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
%            Mellon University. Distributed under the Creative Commons copyleft
%------------------------------------------------------------------------------
thf(b_type,type,(
b: \$tType )).

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

thf(cTHM142_1_pme,conjecture,(
! [Xa: b > a > \$o,Xy: a,Xr: b > \$o] :
( ( Xr
= ( ^ [Xj: b] :
( Xa @ Xj @ Xy ) ) )
=> ? [Xp: ( b > \$o ) > ( b > \$o ) > \$o] :
! [Xs: b > \$o] :
( ! [S: a > \$o] :
( ? [Xt: b] :
( ( Xs @ Xt )
& ( S
= ( Xa @ Xt ) ) )
=> ( S @ Xy ) )
<=> ( Xp @ Xr @ Xs ) ) ) )).

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