## TPTP Problem File: SYO169^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SYO169^5 : TPTP v8.0.0. 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   : 0.25 v7.4.0, 0.33 v7.3.0, 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 unt;   6 typ;   0 def)
%            Number of atoms       :    9 (   0 equ;   0 cnn)
%            Maximal formula atoms :    9 (   9 avg)
%            Number of connectives :   34 (   0   ~;   0   |;   4   &;  26   @)
%                                         (   1 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (  16 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   6 usr;   4 con; 0-3 aty)
%            Number of variables   :    9 (   0   ^   9   !;   0   ?;   9   :)
% 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 ) ) ) ).

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