## TPTP Problem File: SYO248^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SYO248^5 : TPTP v7.1.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem from BASIC-HO-EQ-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1199 [Bro09]

% Status   : Theorem
% Rating   : 0.12 v7.1.0, 0.25 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.43 v6.0.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.60 v4.1.0, 1.00 v4.0.0
% Syntax   : Number of formulae    :   13 (   0 unit;  12 type;   0 defn)
%            Number of atoms       :  160 (  32 equality;  64 variable)
%            Maximal formula depth :   15 (   3 average)
%            Number of connectives :  107 (  12   ~;   5   |;  19   &;  64   @)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  12   :;   0   =)
%            Number of variables   :    1 (   0 sgn;   1   !;   0   ?;   0   ^)
%                                         (   1   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% 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(hh,type,(
hh: \$i )).

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

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

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

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

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

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

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

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

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

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

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

thf(cSIXFRIENDS_AGAIN,conjecture,(
! [P: \$i > \$i > \$o] :
( ( ( ( ( ( P @ a )
= ( P @ aa ) )
& ( ( P @ b )
= ( P @ bb ) )
& ( ( P @ e )
= ( P @ hh ) ) )
=> ( ( P @ c )
= ( P @ dd ) ) )
& ( ( ( ( P @ a )
= ( P @ aa ) )
& ( ( P @ h )
= ( P @ hh ) )
& ( ( P @ b )
= ( P @ cc ) ) )
=> ( ( P @ d )
!= ( P @ ee ) ) )
& ( ( ( ( P @ c )
= ( P @ cc ) )
& ( ( P @ cc )
= ( P @ d ) )
& ( ( P @ d )
= ( P @ dd ) )
& ( ( P @ a )
!= ( P @ bb ) ) )
=> ( ( P @ e )
!= ( P @ hh ) ) )
& ( ( ( ( P @ a )
= ( P @ aa ) )
& ( ( P @ d )
= ( P @ dd ) )
& ( ( P @ b )
!= ( P @ cc ) ) )
=> ( ( P @ e )
= ( P @ hh ) ) )
& ( ( ( ( P @ e )
= ( P @ ee ) )
& ( ( P @ h )
= ( P @ hh ) )
& ( ( P @ c )
= ( P @ dd ) ) )
=> ( ( P @ a )
!= ( P @ bb ) ) )
& ( ( ( ( P @ b )
= ( P @ bb ) )
& ( ( P @ bb )
= ( P @ c ) )
& ( ( P @ c )
= ( P @ cc ) )
& ( ( P @ e )
!= ( P @ hh ) ) )
=> ( ( P @ d )
= ( P @ ee ) ) ) )
=> ( ( ( P @ a )
!= ( P @ aa ) )
| ( ( P @ b )
!= ( P @ bb ) )
| ( ( P @ c )
!= ( P @ cc ) )
| ( ( P @ d )
!= ( P @ dd ) )
| ( ( P @ e )
!= ( P @ ee ) )
| ( ( P @ h )
!= ( P @ hh ) ) ) ) )).

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