## TPTP Problem File: SEV193^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV193^5 : TPTP v7.5.0. 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 unit;   1 type;   0 defn)
%            Number of atoms       :   18 (   0 equality;  13 variable)
%            Maximal formula depth :    9 (   6 average)
%            Number of connectives :   17 (   0   ~;   1   |;   2   &;  10   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :    7 (   0 sgn;   4   !;   1   ?;   2   ^)
%                                         (   7   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% 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 ) ) ) ) )).

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