## TPTP Problem File: SEV238^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV238^5 : TPTP v8.1.2. Released v4.0.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem THM2D
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0480 [Bro09]
%          : THM2D [TPS]

% Status   : Theorem
% Rating   : 0.09 v8.1.0, 0.25 v7.4.0, 0.22 v7.3.0, 0.30 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.25 v6.4.0, 0.29 v6.3.0, 0.33 v6.2.0, 0.17 v6.1.0, 0.33 v6.0.0, 0.17 v5.5.0, 0.20 v5.4.0, 0.25 v4.1.0, 0.67 v4.0.1, 0.33 v4.0.0
% Syntax   : Number of formulae    :    1 (   0 unt;   0 typ;   0 def)
%            Number of atoms       :    0 (   0 equ;   0 cnn)
%            Maximal formula atoms :    0 (   0 avg)
%            Number of connectives :   92 (   0   ~;   0   |;  12   &;  61   @)
%                                         (   1 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (  18 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   14 (  14   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   36 (   8   ^  18   !;  10   ?;  36   :)
% 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
%            Mellon University. Distributed under the Creative Commons copyleft
%          : Polymorphic definitions expanded.
%------------------------------------------------------------------------------
thf(cTHM2D_pme,conjecture,
! [K: ( \$i > \$o ) > \$i > \$o] :
( ( ! [Xx: \$i > \$o] :
( ! [Xx0: \$i] :
( ( Xx @ Xx0 )
=> ? [S: \$i > \$o] :
( ! [Xx1: \$i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) ) )
=> ! [Xx0: \$i] :
( ( K @ Xx @ Xx0 )
=> ( K
@ ^ [Xx1: \$i] :
? [S: \$i > \$o] :
( ! [Xx2: \$i] :
( ( S @ Xx2 )
=> ( K @ S @ Xx2 ) )
& ( S @ Xx1 ) )
@ Xx0 ) ) )
& ( ! [Xx: \$i] :
( ? [S: \$i > \$o] :
( ! [Xx0: \$i] :
( ( S @ Xx0 )
=> ( K @ S @ Xx0 ) )
& ( S @ Xx ) )
=> ( K
@ ^ [Xx0: \$i] :
? [S: \$i > \$o] :
( ! [Xx1: \$i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx ) )
=> ! [Xx: \$i] :
( ( K
@ ^ [Xx0: \$i] :
? [S: \$i > \$o] :
( ! [Xx1: \$i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx )
=> ( K
@ ( K
@ ^ [Xx0: \$i] :
? [S: \$i > \$o] :
( ! [Xx1: \$i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) ) )
@ Xx ) ) ) )
=> ! [Xx: \$i] :
( ( K
@ ^ [Xx0: \$i] :
? [S: \$i > \$o] :
( ! [Xx1: \$i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx )
<=> ( ! [Xx0: \$i] :
( ( K
@ ^ [Xx1: \$i] :
? [S: \$i > \$o] :
( ! [Xx2: \$i] :
( ( S @ Xx2 )
=> ( K @ S @ Xx2 ) )
& ( S @ Xx1 ) )
@ Xx0 )
=> ( K
@ ( K
@ ^ [Xx1: \$i] :
? [S: \$i > \$o] :
( ! [Xx2: \$i] :
( ( S @ Xx2 )
=> ( K @ S @ Xx2 ) )
& ( S @ Xx1 ) ) )
@ Xx0 ) )
& ( K
@ ^ [Xx0: \$i] :
? [S: \$i > \$o] :
( ! [Xx1: \$i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx ) ) ) ) ).

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