## TPTP Problem File: SEV272^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV272^5 : TPTP v7.5.0. Bugfixed v5.2.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem X6007A
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0393 [Bro09]
%          : X6007A [TPS]

% Status   : Theorem
% Rating   : 0.27 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.12 v7.1.0, 0.00 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.2.0
% Syntax   : Number of formulae    :    5 (   0 unit;   2 type;   2 defn)
%            Number of atoms       :   33 (   4 equality;  23 variable)
%            Maximal formula depth :   11 (   7 average)
%            Number of connectives :   24 (   2   ~;   0   |;   4   &;  14   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   25 (  25   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   2   :;   0   =)
%            Number of variables   :   12 (   0 sgn;   4   !;   2   ?;   6   ^)
%                                         (  12   :;   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
%          : Polymorphic definitions expanded.
% Bugfixes : v5.2.0 - Added missing type declarations.
%------------------------------------------------------------------------------
thf(cSUCC_type,type,(
cSUCC: ( ( \$i > \$o ) > \$o ) > ( \$i > \$o ) > \$o )).

thf(cZERO_type,type,(
cZERO: ( \$i > \$o ) > \$o )).

thf(cSUCC_def,definition,
( cSUCC
= ( ^ [Xn: ( \$i > \$o ) > \$o,Xp: \$i > \$o] :
? [Xx: \$i] :
( ( Xp @ Xx )
& ( Xn
@ ^ [Xt: \$i] :
( ( Xt != Xx )
& ( Xp @ Xt ) ) ) ) ) )).

thf(cZERO_def,definition,
( cZERO
= ( ^ [Xp: \$i > \$o] :
~ ( ? [Xx: \$i] :
( Xp @ Xx ) ) ) )).

thf(cX6007A_pme,conjecture,
( ( ^ [N: ( \$i > \$o ) > \$o] :
! [P: ( ( \$i > \$o ) > \$o ) > \$o] :
( ( ( P @ cZERO )
& ! [X: ( \$i > \$o ) > \$o] :
( ( P @ X )
=> ( P @ ( cSUCC @ X ) ) ) )
=> ( P @ N ) ) )
= ( ^ [Xx: ( \$i > \$o ) > \$o] :
! [S: ( ( \$i > \$o ) > \$o ) > \$o] :
( ( ( S @ cZERO )
& ! [X: ( \$i > \$o ) > \$o] :
( ( S @ X )
=> ( S @ ( cSUCC @ X ) ) ) )
=> ( S @ Xx ) ) ) )).

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