## TPTP Problem File: SYO169^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SYO169^5 : TPTP v7.2.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem from BASIC-FO-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0991 [Bro09]

% Status   : Theorem
% Rating   : 0.30 v7.2.0, 0.38 v7.1.0, 0.43 v7.0.0, 0.38 v6.4.0, 0.43 v6.3.0, 0.50 v6.1.0, 0.67 v6.0.0, 0.50 v5.5.0, 0.20 v5.4.0, 0.25 v5.2.0, 0.50 v5.1.0, 0.75 v5.0.0, 0.50 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% Syntax   : Number of formulae    :    7 (   0 unit;   6 type;   0 defn)
%            Number of atoms       :   35 (   0 equality;  17 variable)
%            Maximal formula depth :   16 (   5 average)
%            Number of connectives :   34 (   0   ~;   0   |;   4   &;  26   @)
%                                         (   1 <=>;   3  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6   :;   0   =)
%            Number of variables   :    9 (   0 sgn;   9   !;   0   ?;   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(ab,type,(
ab: \$i )).

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

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

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

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

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

thf(cGRP_COMM,conjecture,
( ( ! [Xx: \$i] :
( cP @ e @ Xx @ Xx )
& ! [Xy: \$i] :
( cP @ Xy @ e @ Xy )
& ! [Xz: \$i] :
( cP @ Xz @ Xz @ e )
& ! [Xx: \$i,Xy: \$i,Xz: \$i,Xxy: \$i,Xyz: \$i,Xxyz: \$i] :
( ( ( cP @ Xx @ Xy @ Xxy )
& ( cP @ Xy @ Xz @ Xyz ) )
=> ( ( cP @ Xxy @ Xz @ Xxyz )
<=> ( cPx @ Xyz @ Xxyz ) ) ) )
=> ( ( cP @ a @ b @ ab )
=> ( cP @ b @ a @ ab ) ) )).

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