## TPTP Problem File: SYO109^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SYO109^5 : TPTP v7.1.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem THM271
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0425 [Bro09]
%          : THM271 [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    :    4 (   0 unit;   3 type;   0 defn)
%            Number of atoms       :   34 (   0 equality;  22 variable)
%            Maximal formula depth :   12 (   6 average)
%            Number of connectives :   33 (   0   ~;   6   |;   2   &;  22   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3   :;   0   =)
%            Number of variables   :    8 (   0 sgn;   6   !;   2   ?;   0   ^)
%                                         (   8   :;   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(cP,type,(
cP: \$i > \$o )).

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

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

thf(cTHM271,conjecture,
( ( ! [Xx: \$i] :
( ? [Xy: \$i] :
( ( cM @ Xx @ Xy )
| ( cN @ Xx @ Xy ) )
=> ( cP @ Xx ) )
& ! [Xw: \$i] :
? [Xu: \$i] :
( ! [Xv: \$i] :
( cM @ Xu @ Xv )
| ( cN @ Xu @ Xw ) )
& ! [Xw: \$i,Xz: \$i] :
( ( ( cM @ Xw @ Xz )
| ( cN @ Xw @ Xz ) )
=> ( ( cM @ Xz @ Xw )
| ( cN @ Xz @ Xw )
| ( cM @ Xz @ Xz )
| ( cN @ Xz @ Xz ) ) ) )
=> ! [Xz: \$i] :
( cP @ Xz ) )).

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