## TPTP Problem File: SEV044^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV044^5 : 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_1114 [Bro09]

% Status   : Theorem
% Rating   : 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.0.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% Syntax   : Number of formulae    :    3 (   0 unit;   2 type;   0 defn)
%            Number of atoms       :   62 (   0 equality;  62 variable)
%            Maximal formula depth :   15 (   6 average)
%            Number of connectives :   61 (   0   ~;   0   |;   4   &;  46   @)
%                                         (   0 <=>;  11  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   2   :;   0   =)
%            Number of variables   :   18 (   0 sgn;  18   !;   0   ?;   0   ^)
%                                         (  18   :;   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(b_type,type,(
b: \$tType )).

thf(a_type,type,(
a: \$tType )).

thf(cTHM506_pme,conjecture,(
! [Xs: b > \$o,Xp: b > a > a > \$o] :
( ! [Xx: b] :
( ( Xs @ Xx )
=> ( ! [Xx0: a,Xy: a] :
( ( Xp @ Xx @ Xx0 @ Xy )
=> ( Xp @ Xx @ Xy @ Xx0 ) )
& ! [Xx0: a,Xy: a,Xz: a] :
( ( ( Xp @ Xx @ Xx0 @ Xy )
& ( Xp @ Xx @ Xy @ Xz ) )
=> ( Xp @ Xx @ Xx0 @ Xz ) ) ) )
=> ( ! [Xx: b > a,Xy: b > a] :
( ! [Xx0: b] :
( ( Xs @ Xx0 )
=> ( Xp @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xx0 ) ) )
=> ! [Xx0: b] :
( ( Xs @ Xx0 )
=> ( Xp @ Xx0 @ ( Xy @ Xx0 ) @ ( Xx @ Xx0 ) ) ) )
& ! [Xx: b > a,Xy: b > a,Xz: b > a] :
( ( ! [Xx0: b] :
( ( Xs @ Xx0 )
=> ( Xp @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xx0 ) ) )
& ! [Xx0: b] :
( ( Xs @ Xx0 )
=> ( Xp @ Xx0 @ ( Xy @ Xx0 ) @ ( Xz @ Xx0 ) ) ) )
=> ! [Xx0: b] :
( ( Xs @ Xx0 )
=> ( Xp @ Xx0 @ ( Xx @ Xx0 ) @ ( Xz @ Xx0 ) ) ) ) ) ) )).

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