## TPTP Problem File: SYO179^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SYO179^5 : 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_1173 [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 v6.0.0, 0.33 v5.5.0, 0.20 v5.4.0, 0.25 v5.2.0, 0.50 v5.1.0, 0.75 v5.0.0, 0.25 v4.1.0, 0.67 v4.0.0
% Syntax   : Number of formulae    :    9 (   0 unit;   8 type;   0 defn)
%            Number of atoms       :  108 (   0 equality;  12 variable)
%            Maximal formula depth :   19 (   4 average)
%            Number of connectives :  107 (   0   ~;  16   |;  18   &;  72   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8   :;   0   =)
%            Number of variables   :    6 (   0 sgn;   0   !;   6   ?;   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
%            Mellon University. Distributed under the Creative Commons copyleft
%          :
%------------------------------------------------------------------------------
thf(cG,type,(
cG: \$i > \$i > \$o )).

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

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

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

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

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

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

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

thf(cSIX_THEOREM_B,conjecture,
( ( ( ( cR @ cA @ cB )
| ( cG @ cA @ cB ) )
& ( ( cR @ cA @ cC )
| ( cG @ cA @ cC ) )
& ( ( cR @ cA @ cD )
| ( cG @ cA @ cD ) )
& ( ( cR @ cA @ cE )
| ( cG @ cA @ cE ) )
& ( ( cR @ cA @ cF )
| ( cG @ cA @ cF ) )
& ( ( cR @ cB @ cC )
| ( cG @ cB @ cC ) )
& ( ( cR @ cB @ cD )
| ( cG @ cB @ cD ) )
& ( ( cR @ cB @ cE )
| ( cG @ cB @ cE ) )
& ( ( cR @ cB @ cF )
| ( cG @ cB @ cF ) )
& ( ( cR @ cC @ cD )
| ( cG @ cC @ cD ) )
& ( ( cR @ cC @ cE )
| ( cG @ cC @ cE ) )
& ( ( cR @ cC @ cF )
| ( cG @ cC @ cF ) )
& ( ( cR @ cD @ cE )
| ( cG @ cD @ cE ) )
& ( ( cR @ cD @ cF )
| ( cG @ cD @ cF ) )
& ( ( cR @ cE @ cF )
| ( cG @ cE @ cF ) ) )
=> ( ? [Xa: \$i,Xb: \$i,Xc: \$i] :
( ( cR @ Xa @ Xb )
& ( cR @ Xa @ Xc )
& ( cR @ Xb @ Xc ) )
| ? [Xa: \$i,Xb: \$i,Xc: \$i] :
( ( cG @ Xa @ Xb )
& ( cG @ Xa @ Xc )
& ( cG @ Xb @ Xc ) ) ) )).

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