## TPTP Problem File: SYO113^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SYO113^5 : TPTP v7.1.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem THM350
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0484 [Bro09]
%          : THM350 [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 v6.0.0, 0.17 v5.5.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    6 (   0 unit;   5 type;   0 defn)
%            Number of atoms       :   47 (   0 equality;  14 variable)
%            Maximal formula depth :   16 (   5 average)
%            Number of connectives :   46 (   0   ~;   1   |;  10   &;  29   @)
%                                         (   1 <=>;   5  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5   :;   0   =)
%            Number of variables   :    6 (   0 sgn;   6   !;   0   ?;   0   ^)
%                                         (   6   :;   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(cNUMBER,type,(
cNUMBER: \$i > \$o )).

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

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

thf(cS,type,(
cS: \$i > \$i )).

thf(c0,type,(
c0: \$i )).

thf(cTHM350,conjecture,
( ( ( cEVEN @ c0 )
& ! [Xn: \$i] :
( ( cEVEN @ Xn )
=> ( cEVEN @ ( cS @ ( cS @ Xn ) ) ) )
& ( cODD @ ( cS @ c0 ) )
& ! [Xn: \$i] :
( ( cODD @ Xn )
=> ( cODD @ ( cS @ ( cS @ Xn ) ) ) )
& ( ( ( cNUMBER @ c0 )
& ( cNUMBER @ ( cS @ c0 ) )
& ! [Xx: \$i] :
( ( ( cNUMBER @ Xx )
& ( cNUMBER @ ( cS @ Xx ) ) )
=> ( ( cNUMBER @ ( cS @ Xx ) )
& ( cNUMBER @ ( cS @ ( cS @ Xx ) ) ) ) ) )
=> ! [Xx: \$i] :
( ( cNUMBER @ Xx )
& ( cNUMBER @ ( cS @ Xx ) ) ) )
& ! [Xn: \$i] :
( ( cNUMBER @ Xn )
<=> ( ( cEVEN @ Xn )
| ( cODD @ Xn ) ) ) )
=> ! [Xn: \$i] :
( cNUMBER @ Xn ) )).

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