## TPTP Problem File: SEV182^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV182^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem from CANTOR-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0949 [Bro09]

% Status   : Unknown
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :    1 (   0 unit;   0 type;   0 defn)
%            Number of atoms       :   26 (   3 equality;  23 variable)
%            Maximal formula depth :   16 (  16 average)
%            Number of connectives :   20 (   1   ~;   0   |;   3   &;  11   @)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    2 (   0   :;   0   =)
%            Number of variables   :   12 (   0 sgn;   6   !;   3   ?;   3   ^)
%                                         (  12   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_UNK_EQU_NAR

% Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
%            project in the Department of Mathematical Sciences at Carnegie
%------------------------------------------------------------------------------
thf(cTHM110_pme,conjecture,(
! [S: \$i > \$o] :
~ ( ? [Z: \$i > \$o] :
( ! [Xx: \$i] :
( ( Z @ Xx )
=> ( S @ Xx ) )
& ? [Xs: ( \$i > \$o ) > \$i] :
( ! [Xx: \$i > \$o] :
( ! [Xx0: \$i] :
( ( Xx @ Xx0 )
=> ( S @ Xx0 ) )
=> ( Z @ ( Xs @ Xx ) ) )
& ! [Xy: \$i] :
( ( Z @ Xy )
=> ? [Xy0: \$i > \$o] :
( ( ^ [Xx: \$i > \$o] :
( ! [Xx0: \$i] :
( ( Xx @ Xx0 )
=> ( S @ Xx0 ) )
& ( Xy
= ( Xs @ Xx ) ) ) )
= ( ^ [Xx: \$i > \$o,Xy: \$i > \$o] : ( Xx = Xy )
@ Xy0 ) ) ) ) ) ) )).

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