## TPTP Problem File: SEV193^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV193^5 : TPTP v8.0.0. Released v4.0.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem from S-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0896 [Bro09]

% Status   : Unknown
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unt;   1 typ;   0 def)
%            Number of atoms       :    5 (   0 equ;   0 cnn)
%            Maximal formula atoms :    5 (   5 avg)
%            Number of connectives :   17 (   0   ~;   1   |;   2   &;  10   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    1 (   1 usr;   0 con; 1-1 aty)
%            Number of variables   :    7 (   2   ^   4   !;   1   ?;   7   :)
% SPC      : TH0_UNK_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(cT,type,
cT: ( \$i > \$o ) > \$o ).

thf(cTHM501_pme,conjecture,
( ! [S: ( \$i > \$o ) > \$o] :
( ! [Xx: \$i > \$o] :
( ( S @ Xx )
=> ( cT @ Xx ) )
=> ( cT
@ ^ [Xx: \$i] :
? [S0: \$i > \$o] :
( ( S @ S0 )
& ( S0 @ Xx ) ) ) )
=> ! [U: \$i > \$o,V: \$i > \$o] :
( ( ( cT @ U )
& ( cT @ V ) )
=> ( cT
@ ^ [Xz: \$i] :
( ( U @ Xz )
| ( V @ Xz ) ) ) ) ) ).

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