## TPTP Problem File: SEV292^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV292^5 : TPTP v7.5.0. Bugfixed v6.2.0.
% Domain   : Set Theory
% Problem  : TPS problem BLEDSOE7A
% Version  : Especial.
% English  :

% Refs     : [BF93]  Bledsoe & Feng (1993), SET-VAR
%          : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0340 [Bro09]
%          : BLEDSOE7A [TPS]

% Status   : Theorem
% Rating   : 0.45 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0
% Syntax   : Number of formulae    :   10 (   0 unit;   5 type;   4 defn)
%            Number of atoms       :   40 (   5 equality;  20 variable)
%            Maximal formula depth :   11 (   6 average)
%            Number of connectives :   27 (   2   ~;   0   |;   5   &;  17   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   33 (  33   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5   :;   0   =)
%            Number of variables   :   11 (   0 sgn;   2   !;   3   ?;   6   ^)
%                                         (  11   :;   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
% Bugfixes : v5.2.0 - Added missing type declarations.
%          : v6.2.0 - Reordered definitions.
%------------------------------------------------------------------------------
thf(cP_type,type,(
cP: ( ( \$i > \$o ) > \$o ) > \$o )).

thf(cONE_type,type,(
cONE: ( \$i > \$o ) > \$o )).

thf(cSUCC_type,type,(
cSUCC: ( ( \$i > \$o ) > \$o ) > ( \$i > \$o ) > \$o )).

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

thf(c_less__eq__type,type,(
c_less__eq_: ( ( \$i > \$o ) > \$o ) > ( ( \$i > \$o ) > \$o ) > \$o )).

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

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

thf(cONE_def,definition,
( cONE
= ( cSUCC @ cZERO ) )).

thf(c_less__eq__def,definition,
( c_less__eq_
= ( ^ [Xx: ( \$i > \$o ) > \$o,Xy: ( \$i > \$o ) > \$o] :
! [Xp: ( ( \$i > \$o ) > \$o ) > \$o] :
( ( ( Xp @ Xx )
& ! [Xz: ( \$i > \$o ) > \$o] :
( ( Xp @ Xz )
=> ( Xp @ ( cSUCC @ Xz ) ) ) )
=> ( Xp @ Xy ) ) ) )).

thf(cBLEDSOE7A,conjecture,
( ( cP @ cONE )
=> ? [Xx: ( \$i > \$o ) > \$o] :
( ( c_less__eq_ @ cZERO @ Xx )
& ( c_less__eq_ @ Xx @ ( cSUCC @ cONE ) )
& ( cP @ Xx ) ) )).

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