## TPTP Problem File: SEV066^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV066^5 : TPTP v7.2.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem THM120D
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0439 [Bro09]
%          : THM120D [TPS]

% Status   : Theorem
% Rating   : 0.70 v7.2.0, 0.62 v7.1.0, 0.57 v7.0.0, 0.62 v6.4.0, 0.57 v6.3.0, 0.67 v5.5.0, 0.60 v5.4.0, 0.50 v4.1.0, 0.67 v4.0.0
% Syntax   : Number of formulae    :    1 (   0 unit;   0 type;   0 defn)
%            Number of atoms       :   40 (   0 equality;  36 variable)
%            Maximal formula depth :   15 (  15 average)
%            Number of connectives :   40 (   1   ~;   5   |;   3   &;  30   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   14 (  14   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   0   :;   0   =)
%            Number of variables   :   15 (   4 sgn;   9   !;   2   ?;   4   ^)
%                                         (  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(cTHM120D_pme,conjecture,(
? [Xr_28: ( \$i > \$o ) > ( \$i > \$o ) > \$i > \$o,Xr_27: ( \$i > \$o ) > ( \$i > \$o ) > \$i > \$o] :
( ! [Xx: \$i > \$o,Xw_2: \$i] :
( ( Xr_27 @ Xx @ Xx @ Xw_2 )
| ( Xr_28 @ Xx @ Xx @ Xw_2 ) )
& ! [Xx: \$i > \$o,Xy: \$i > \$o,Xz: \$i > \$o] :
( ( ! [Xw_2: \$i] :
( ( Xr_27 @ Xx @ Xy @ Xw_2 )
| ( Xr_28 @ Xx @ Xy @ Xw_2 ) )
& ! [Xw_2: \$i] :
( ( Xr_27 @ Xy @ Xz @ Xw_2 )
| ( Xr_28 @ Xy @ Xz @ Xw_2 ) ) )
=> ! [Xw_2: \$i] :
( ( Xr_27 @ Xx @ Xz @ Xw_2 )
| ( Xr_28 @ Xx @ Xz @ Xw_2 ) ) )
& ~ ( ! [Xw_2: \$i] :
( ( Xr_27
@ ^ [Xx: \$i] : \$true
@ ^ [Xx: \$i] : \$false
@ Xw_2 )
| ( Xr_28
@ ^ [Xx: \$i] : \$true
@ ^ [Xx: \$i] : \$false
@ Xw_2 ) ) ) ) )).

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