## TPTP Problem File: SEV108^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV108^5 : TPTP v8.2.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem from RELN-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1163 [Bro09]

% Status   : Theorem
% Rating   : 0.50 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.57 v7.4.0, 0.33 v7.2.0, 0.25 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.57 v6.1.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.80 v4.1.0, 1.00 v4.0.0
% Syntax   : Number of formulae    :    1 (   0 unt;   0 typ;   0 def)
%            Number of atoms       :   18 (  18 equ;   0 cnn)
%            Maximal formula atoms :   18 (  18 avg)
%            Number of connectives :   62 (  21   ~;   1   |;  22   &;  16   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   25 (  25 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    1 (   0 usr;   0 con; 2-2 aty)
%            Number of variables   :   12 (   0   ^;   9   !;   3   ?;  12   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
%            project in the Department of Mathematical Sciences at Carnegie
%------------------------------------------------------------------------------
thf(cSIX_THEOREM_pme,conjecture,
! [R: \$i > \$i > \$o,A: \$i,B: \$i,C: \$i,D: \$i,E: \$i,F: \$i] :
( ( ! [Xx: \$i,Xy: \$i] :
( ( R @ Xx @ Xy )
=> ( R @ Xy @ Xx ) )
& ( A != B )
& ( A != C )
& ( A != D )
& ( A != E )
& ( A != F )
& ( B != C )
& ( B != D )
& ( B != E )
& ( B != F )
& ( C != D )
& ( C != E )
& ( C != F )
& ( D != E )
& ( D != F )
& ( E != F ) )
=> ? [Xa: \$i,Xb: \$i,Xc: \$i] :
( ( Xa != Xb )
& ( Xa != Xc )
& ( Xb != Xc )
& ( ( ( R @ Xa @ Xb )
& ( R @ Xa @ Xc )
& ( R @ Xb @ Xc ) )
| ( ~ ( R @ Xa @ Xb )
& ~ ( R @ Xa @ Xc )
& ~ ( R @ Xb @ Xc ) ) ) ) ) ).

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