## TPTP Problem File: SEV046^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV046^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem from PERS-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1181 [Bro09]

% Status   : Theorem
% Rating   : 0.18 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.1.0, 0.60 v4.1.0, 0.33 v4.0.1, 1.00 v4.0.0
% Syntax   : Number of formulae    :    3 (   0 unit;   2 type;   0 defn)
%            Number of atoms       :   91 (   1 equality;  90 variable)
%            Maximal formula depth :   18 (   7 average)
%            Number of connectives :   88 (   0   ~;   0   |;   8   &;  66   @)
%                                         (   0 <=>;  14  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   2   :;   0   =)
%            Number of variables   :   30 (   0 sgn;  30   !;   0   ?;   0   ^)
%                                         (  30   :;   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(a_type,type,(
a: \$tType )).

thf(b_type,type,(
b: \$tType )).

thf(cTHM507_pme,conjecture,(
! [Xp: a > a > \$o,Xp2: a > b > b > \$o] :
( ( ! [Xx: a,Xy: a] :
( ( Xp @ Xx @ Xy )
=> ( Xp @ Xy @ Xx ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( ( Xp @ Xx @ Xy )
& ( Xp @ Xy @ Xz ) )
=> ( Xp @ Xx @ Xz ) )
& ! [Xx: a] :
( ( Xp @ Xx @ Xx )
=> ( ! [Xx0: b,Xy: b] :
( ( Xp2 @ Xx @ Xx0 @ Xy )
=> ( Xp2 @ Xx @ Xy @ Xx0 ) )
& ! [Xx0: b,Xy: b,Xz: b] :
( ( ( Xp2 @ Xx @ Xx0 @ Xy )
& ( Xp2 @ Xx @ Xy @ Xz ) )
=> ( Xp2 @ Xx @ Xx0 @ Xz ) ) ) )
& ! [Xx: a,Xy: a] :
( ( Xp @ Xx @ Xy )
=> ( ( Xp2 @ Xx )
= ( Xp2 @ Xy ) ) ) )
=> ( ! [Xx: a > b,Xy: a > b] :
( ! [Xx0: a,Xy0: a] :
( ( Xp @ Xx0 @ Xy0 )
=> ( Xp2 @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xy0 ) ) )
=> ! [Xx0: a,Xy0: a] :
( ( Xp @ Xx0 @ Xy0 )
=> ( Xp2 @ Xx0 @ ( Xy @ Xx0 ) @ ( Xx @ Xy0 ) ) ) )
& ! [Xx: a > b,Xy: a > b,Xz: a > b] :
( ( ! [Xx0: a,Xy0: a] :
( ( Xp @ Xx0 @ Xy0 )
=> ( Xp2 @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xy0 ) ) )
& ! [Xx0: a,Xy0: a] :
( ( Xp @ Xx0 @ Xy0 )
=> ( Xp2 @ Xx0 @ ( Xy @ Xx0 ) @ ( Xz @ Xy0 ) ) ) )
=> ! [Xx0: a,Xy0: a] :
( ( Xp @ Xx0 @ Xy0 )
=> ( Xp2 @ Xx0 @ ( Xx @ Xx0 ) @ ( Xz @ Xy0 ) ) ) ) ) ) )).

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