## TPTP Problem File: SEV100^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV100^5 : TPTP v7.2.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem from RELN-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1088 [Bro09]

% Status   : Theorem
% Rating   : 0.80 v7.2.0, 0.75 v7.1.0, 0.71 v7.0.0, 0.75 v6.4.0, 0.71 v6.3.0, 0.83 v5.5.0, 0.80 v5.4.0, 0.75 v5.2.0, 1.00 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   44 (   0 equality;  36 variable)
%            Maximal formula depth :   14 (   8 average)
%            Number of connectives :   48 (   5   ~;   7   |;   5   &;  30   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   14 (  14   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   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
%            Mellon University. Distributed under the Creative Commons copyleft
%          :
%------------------------------------------------------------------------------
thf(p,type,(
p: \$o )).

thf(cTHM120F_pme,conjecture,(
? [Xr_28: ( \$i > \$o ) > ( \$i > \$o ) > \$i > \$o,Xr_27: ( \$i > \$o ) > ( \$i > \$o ) > \$i > \$o] :
( ! [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 ) ) )
& ! [Xx: \$i > \$o,Xw_2: \$i] :
( ( Xr_27 @ Xx @ Xx @ Xw_2 )
| ( Xr_28 @ Xx @ Xx @ Xw_2 ) )
& ~ ( ! [Xw_2: \$i] :
( ( Xr_27
@ ^ [Xx: \$i] :
( p
| ~ ( p ) )
@ ^ [Xx: \$i] :
( p
& ~ ( p ) )
@ Xw_2 )
| ( Xr_28
@ ^ [Xx: \$i] :
( p
| ~ ( p ) )
@ ^ [Xx: \$i] :
( p
& ~ ( p ) )
@ Xw_2 ) ) ) ) )).

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