## TPTP Problem File: SEV090^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV090^5 : TPTP v7.5.0. 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_1016 [Bro09]

% Status   : Unknown
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   30 (   0 equality;  30 variable)
%            Maximal formula depth :   12 (   7 average)
%            Number of connectives :   31 (   2   ~;   0   |;   6   &;  20   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :   14 (   0 sgn;  10   !;   4   ?;   0   ^)
%                                         (  14   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_UNK_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(a_type,type,(
a: \$tType )).

thf(cTHM165_pme,conjecture,
( ? [Xr: a > a > \$o] :
( ! [Xx: a] :
? [Xw: a] :
( Xr @ Xx @ Xw )
& ! [Xx: a] :
~ ( Xr @ Xx @ Xx )
& ! [Xx: a,Xy: a,Xz: a] :
( ( ( Xr @ Xx @ Xy )
& ( Xr @ Xy @ Xz ) )
=> ( Xr @ Xx @ Xz ) ) )
=> ? [R: ( a > \$o ) > ( a > \$o ) > \$o] :
( ! [Xx: a > \$o] :
? [Xw: a > \$o] :
( R @ Xx @ Xw )
& ! [Xx: a > \$o] :
~ ( R @ Xx @ Xx )
& ! [Xx: a > \$o,Xy: a > \$o,Xz: a > \$o] :
( ( ( R @ Xx @ Xy )
& ( R @ Xy @ Xz ) )
=> ( R @ Xx @ Xz ) ) ) )).

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