## TPTP Problem File: SEV068^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV068^5 : TPTP v7.2.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem THM275A-1
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0448 [Bro09]
%          : THM275A-1 [TPS]

% Status   : Theorem
% Rating   : 0.90 v7.2.0, 0.88 v7.1.0, 0.86 v7.0.0, 0.88 v6.4.0, 0.86 v6.3.0, 0.83 v5.5.0, 0.80 v5.4.0, 0.75 v4.1.0, 0.67 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   36 (   0 equality;  36 variable)
%            Maximal formula depth :   15 (   8 average)
%            Number of connectives :   35 (   0   ~;   0   |;   5   &;  24   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :   15 (   0 sgn;  14   !;   1   ?;   0   ^)
%                                         (  15   :;   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
%          : Polymorphic definitions expanded.
%          :
%------------------------------------------------------------------------------
thf(a_type,type,(
a: \$tType )).

thf(cTHM275A_1_pme,conjecture,(
! [Xr: a > a > \$o] :
? [Xp: a > a > \$o] :
( ! [Xx: a,Xy: a] :
( ( Xr @ Xx @ Xy )
=> ( Xp @ Xx @ Xy ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( ( Xp @ Xx @ Xy )
& ( Xp @ Xy @ Xz ) )
=> ( Xp @ Xx @ Xz ) )
& ! [Xq: a > a > \$o] :
( ( ! [Xx: a,Xy: a,Xz: a] :
( ( ( Xq @ Xx @ Xy )
& ( Xq @ Xy @ Xz ) )
=> ( Xq @ Xx @ Xz ) )
& ! [Xx: a,Xy: a] :
( ( Xr @ Xx @ Xy )
=> ( Xq @ Xx @ Xy ) ) )
=> ! [Xx: a,Xy: a] :
( ( Xp @ Xx @ Xy )
=> ( Xq @ Xx @ Xy ) ) ) ) )).

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