## TPTP Problem File: SEV382^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV382^5 : TPTP v7.1.0. Released v4.0.0.
% Domain   : Set Theory
% Problem  : TPS problem TRANS-IND
% Version  : Especial.
% English  : Transfinite induction theorem, from [BB93].

% Refs     : [BB93]  Bailin & Barker-Plummer (1993), L-match: An Inference
%          : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0328 [Bro09]
%          : TRANS-IND [TPS]

% Status   : Theorem
% Rating   : 0.25 v7.1.0, 0.29 v7.0.0, 0.25 v6.4.0, 0.29 v6.3.0, 0.33 v6.2.0, 0.50 v6.1.0, 0.33 v6.0.0, 0.17 v5.5.0, 0.00 v5.1.0, 0.25 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   18 (   0 equality;  18 variable)
%            Maximal formula depth :   13 (   8 average)
%            Number of connectives :   18 (   1   ~;   0   |;   2   &;  10   @)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :    9 (   0 sgn;   7   !;   2   ?;   0   ^)
%                                         (   9   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_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(a_type,type,(
a: \$tType )).

thf(cTRANS_IND,conjecture,(
! [Xr: a > a > \$o,P: a > \$o] :
( ( ! [Xs: a > \$o] :
( ? [Xz: a] :
( Xs @ Xz )
=> ? [Xy: a] :
( ( Xs @ Xy )
& ! [Xw: a] :
( ( Xr @ Xw @ Xy )
=> ~ ( Xs @ Xw ) ) ) )
& ! [Xx: a] :
( ! [Xy: a] :
( ( Xr @ Xy @ Xx )
=> ( P @ Xy ) )
=> ( P @ Xx ) ) )
=> ! [Xx: a] :
( P @ Xx ) ) )).

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