TPTP Problem File: NUM831^5.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : NUM831^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% Domain : Number Theory (Induction on naturals)
% Problem : TPS problem from PETER-THMS
% Version : Especial.
% English :
% Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_0997 [Bro09]
% Status : Unknown
% Rating : 1.00 v5.2.0
% Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% Number of atoms : 7 ( 5 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 34 ( 1 ~; 0 |; 6 &; 21 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 12 ( 0 ^; 10 !; 2 ?; 12 :)
% 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
% Mellon University. Distributed under the Creative Commons copyleft
% license: http://creativecommons.org/licenses/by-sa/3.0/
% :
% Bugfixes : v5.2.0 - Added missing type declarations.
%------------------------------------------------------------------------------
thf(c0_type,type,
c0: $i ).
thf(cS_type,type,
cS: $i > $i ).
thf(cIND_type,type,
cIND: $o ).
thf(cIND_def,definition,
( cIND
= ( ! [Xp: $i > $o] :
( ( ( Xp @ c0 )
& ! [Xx: $i] :
( ( Xp @ Xx )
=> ( Xp @ ( cS @ Xx ) ) ) )
=> ! [Xx: $i] : ( Xp @ Xx ) ) ) ) ).
thf(cTHM606_pme,conjecture,
( ( cIND
& ! [Xx: $i,Xy: $i] :
( ( ( cS @ Xx )
= ( cS @ Xy ) )
=> ( Xx = Xy ) )
& ! [Xn: $i] :
( ( cS @ Xn )
!= c0 ) )
=> ? [Xd: $i > $i > $o] :
( ( Xd @ c0 @ c0 )
& ! [Xx: $i,Xy: $i] :
( ( Xd @ Xx @ Xy )
=> ( Xd @ ( cS @ Xx ) @ ( cS @ ( cS @ Xy ) ) ) )
& ! [Xx: $i] :
? [X: $i] :
( ( Xd @ Xx @ X )
& ! [Y: $i] :
( ( Xd @ Xx @ Y )
=> ( X = Y ) ) ) ) ) ).
%------------------------------------------------------------------------------