## TPTP Problem File: SEV141^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV141^5 : TPTP v7.2.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem THM250
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0537 [Bro09]
%          : tps_0538 [Bro09]
%          : tps_1172 [Bro09]
%          : THM250 [TPS]

% Status   : Theorem
% Rating   : 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.71 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.43 v6.1.0, 0.71 v5.5.0, 0.67 v5.4.0, 0.60 v4.1.0, 0.67 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   73 (   1 equality;  72 variable)
%            Maximal formula depth :   23 (  12 average)
%            Number of connectives :   70 (   0   ~;   2   |;   8   &;  48   @)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :   30 (   0 sgn;  26   !;   0   ?;   4   ^)
%                                         (  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
%          : Polymorphic definitions expanded.
%          :
%------------------------------------------------------------------------------
thf(a_type,type,(
a: \$tType )).

thf(cTHM250_pme,conjecture,(
! [R: a > a > \$o,S: a > a > \$o] :
( ( ^ [Xx1: a,Xy1: a] :
! [Xp1: a > a > \$o] :
( ( ! [Xx: a,Xy: a] :
( ( ( R @ Xx @ Xy )
| ( S @ Xx @ Xy ) )
=> ( Xp1 @ Xx @ Xy ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( ( Xp1 @ Xx @ Xy )
& ( Xp1 @ Xy @ Xz ) )
=> ( Xp1 @ Xx @ Xz ) ) )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
= ( ^ [Xx1: a,Xy1: a] :
! [Xp1: a > a > \$o] :
( ( ! [Xx: a,Xy: a] :
( ( ! [Xp10: a > a > \$o] :
( ( ! [Xx0: a,Xy0: a] :
( ( R @ Xx0 @ Xy0 )
=> ( Xp10 @ Xx0 @ Xy0 ) )
& ! [Xx0: a,Xy0: a,Xz: a] :
( ( ( Xp10 @ Xx0 @ Xy0 )
& ( Xp10 @ Xy0 @ Xz ) )
=> ( Xp10 @ Xx0 @ Xz ) ) )
=> ( Xp10 @ Xx @ Xy ) )
| ! [Xp10: a > a > \$o] :
( ( ! [Xx0: a,Xy0: a] :
( ( S @ Xx0 @ Xy0 )
=> ( Xp10 @ Xx0 @ Xy0 ) )
& ! [Xx0: a,Xy0: a,Xz: a] :
( ( ( Xp10 @ Xx0 @ Xy0 )
& ( Xp10 @ Xy0 @ Xz ) )
=> ( Xp10 @ Xx0 @ Xz ) ) )
=> ( Xp10 @ Xx @ Xy ) ) )
=> ( Xp1 @ Xx @ Xy ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( ( Xp1 @ Xx @ Xy )
& ( Xp1 @ Xy @ Xz ) )
=> ( Xp1 @ Xx @ Xz ) ) )
=> ( Xp1 @ Xx1 @ Xy1 ) ) ) ) )).

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