## TPTP Problem File: SYO387^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SYO387^5 : TPTP v7.2.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem THM409-4
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0578 [Bro09]
%          : THM409-4 [TPS]

% 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 v5.1.0, 0.50 v5.0.0, 0.25 v4.1.0, 0.67 v4.0.0
% Syntax   : Number of formulae    :   15 (   0 unit;  14 type;   0 defn)
%            Number of atoms       :  164 (   0 equality;  71 variable)
%            Maximal formula depth :   41 (   6 average)
%            Number of connectives :  185 (  22   ~;  20   |;  25   &; 118   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   24 (  24   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  14   :;   0   =)
%            Number of variables   :   39 (   0 sgn;  39   !;   0   ?;   0   ^)
%                                         (  39   :;   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_5,type,(
cQ_5: \$i > \$i > \$i > \$o )).

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

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

thf(cQ_4,type,(
cQ_4: \$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_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_4,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 ) )
& ! [Xx: \$i,Xy: \$i,Xz: \$i] :
~ ( cQ_5 @ Xx @ Xy @ Xz ) ) )).

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