## TPTP Problem File: SYO391^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SYO391^5 : TPTP v7.1.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem from MISC
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1245 [Bro09]

% Status   : Theorem
% Rating   : 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 v5.1.0, 0.50 v5.0.0, 0.25 v4.1.0, 0.67 v4.0.0
% Syntax   : Number of formulae    :   19 (   0 unit;  18 type;   0 defn)
%            Number of atoms       :  242 (   0 equality; 105 variable)
%            Maximal formula depth :   53 (   6 average)
%            Number of connectives :  273 (  32   ~;  30   |;  37   &; 174   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   34 (  34   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   20 (  18   :;   0   =)
%            Number of variables   :   57 (   0 sgn;  57   !;   0   ?;   0   ^)
%                                         (  57   :;   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(cQ_7,type,(
cQ_7: \$i > \$i > \$i > \$o )).

thf(f,type,(
f: \$i > \$i )).

thf(cP_6,type,(
cP_6: \$i > \$i > \$o )).

thf(cQ_6,type,(
cQ_6: \$i > \$i > \$i > \$o )).

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

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

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

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

thf(cP_5,type,(
cP_5: \$i > \$i > \$o )).

thf(cQ_5,type,(
cQ_5: \$i > \$i > \$i > \$o )).

thf(cP_4,type,(
cP_4: \$i > \$i > \$o )).

thf(cQ_4,type,(
cQ_4: \$i > \$i > \$i > \$o )).

thf(cP_3,type,(
cP_3: \$i > \$i > \$o )).

thf(cQ_3,type,(
cQ_3: \$i > \$i > \$i > \$o )).

thf(cP_2,type,(
cP_2: \$i > \$i > \$o )).

thf(cQ_2,type,(
cQ_2: \$i > \$i > \$i > \$o )).

thf(cP_1,type,(
cP_1: \$i > \$i > \$o )).

thf(cQ_1,type,(
cQ_1: \$i > \$i > \$i > \$o )).

thf(cTHM409_6,conjecture,(
~ ( ( cQ_1 @ a @ b @ c )
& ( cP_1 @ a @ a )
& ( cP_1 @ b @ b )
& ( cP_1 @ c @ c )
& ! [Xx: \$i] :
( cP_1 @ d @ Xx )
& ! [Xx: \$i,Xy: \$i] :
( ~ ( cP_1 @ Xx @ Xy )
| ( cP_1 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: \$i,Xy: \$i,Xz: \$i,Xu: \$i,Xv: \$i,Xw: \$i] :
( ~ ( cQ_1 @ Xx @ Xy @ Xz )
| ~ ( cP_1 @ ( f @ Xx ) @ Xu )
| ~ ( cP_1 @ ( f @ Xy ) @ Xv )
| ~ ( cP_1 @ ( f @ Xz ) @ Xw )
| ( cQ_2 @ Xu @ Xv @ Xw ) )
& ( cP_2 @ a @ a )
& ( cP_2 @ b @ b )
& ( cP_2 @ c @ c )
& ! [Xx: \$i] :
( cP_2 @ d @ Xx )
& ! [Xx: \$i,Xy: \$i] :
( ~ ( cP_2 @ Xx @ Xy )
| ( cP_2 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: \$i,Xy: \$i,Xz: \$i,Xu: \$i,Xv: \$i,Xw: \$i] :
( ~ ( cQ_2 @ Xx @ Xy @ Xz )
| ~ ( cP_2 @ ( f @ Xx ) @ Xu )
| ~ ( cP_2 @ ( f @ Xy ) @ Xv )
| ~ ( cP_2 @ ( f @ Xz ) @ Xw )
| ( cQ_3 @ Xu @ Xv @ Xw ) )
& ( cP_3 @ a @ a )
& ( cP_3 @ b @ b )
& ( cP_3 @ c @ c )
& ! [Xx: \$i] :
( cP_3 @ d @ Xx )
& ! [Xx: \$i,Xy: \$i] :
( ~ ( cP_3 @ Xx @ Xy )
| ( cP_3 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: \$i,Xy: \$i,Xz: \$i,Xu: \$i,Xv: \$i,Xw: \$i] :
( ~ ( cQ_3 @ Xx @ Xy @ Xz )
| ~ ( cP_3 @ ( f @ Xx ) @ Xu )
| ~ ( cP_3 @ ( f @ Xy ) @ Xv )
| ~ ( cP_3 @ ( f @ Xz ) @ Xw )
| ( cQ_4 @ Xu @ Xv @ Xw ) )
& ( cP_4 @ a @ a )
& ( cP_4 @ b @ b )
& ( cP_4 @ c @ c )
& ! [Xx: \$i] :
( cP_4 @ d @ Xx )
& ! [Xx: \$i,Xy: \$i] :
( ~ ( cP_4 @ Xx @ Xy )
| ( cP_4 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: \$i,Xy: \$i,Xz: \$i,Xu: \$i,Xv: \$i,Xw: \$i] :
( ~ ( cQ_4 @ Xx @ Xy @ Xz )
| ~ ( cP_4 @ ( f @ Xx ) @ Xu )
| ~ ( cP_4 @ ( f @ Xy ) @ Xv )
| ~ ( cP_4 @ ( f @ Xz ) @ Xw )
| ( cQ_5 @ Xu @ Xv @ Xw ) )
& ( cP_5 @ a @ a )
& ( cP_5 @ b @ b )
& ( cP_5 @ c @ c )
& ! [Xx: \$i] :
( cP_5 @ d @ Xx )
& ! [Xx: \$i,Xy: \$i] :
( ~ ( cP_5 @ Xx @ Xy )
| ( cP_5 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: \$i,Xy: \$i,Xz: \$i,Xu: \$i,Xv: \$i,Xw: \$i] :
( ~ ( cQ_5 @ Xx @ Xy @ Xz )
| ~ ( cP_5 @ ( f @ Xx ) @ Xu )
| ~ ( cP_5 @ ( f @ Xy ) @ Xv )
| ~ ( cP_5 @ ( f @ Xz ) @ Xw )
| ( cQ_6 @ Xu @ Xv @ Xw ) )
& ( cP_6 @ a @ a )
& ( cP_6 @ b @ b )
& ( cP_6 @ c @ c )
& ! [Xx: \$i] :
( cP_6 @ d @ Xx )
& ! [Xx: \$i,Xy: \$i] :
( ~ ( cP_6 @ Xx @ Xy )
| ( cP_6 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: \$i,Xy: \$i,Xz: \$i,Xu: \$i,Xv: \$i,Xw: \$i] :
( ~ ( cQ_6 @ Xx @ Xy @ Xz )
| ~ ( cP_6 @ ( f @ Xx ) @ Xu )
| ~ ( cP_6 @ ( f @ Xy ) @ Xv )
| ~ ( cP_6 @ ( f @ Xz ) @ Xw )
| ( cQ_7 @ Xu @ Xv @ Xw ) )
& ! [Xx: \$i,Xy: \$i,Xz: \$i] :
~ ( cQ_7 @ Xx @ Xy @ Xz ) ) )).

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