## TPTP Problem File: SEV118^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV118^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem from PER-CLOSURE-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1081 [Bro09]

% Status   : Unknown
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   44 (   0 equality;  44 variable)
%            Maximal formula depth :   16 (   9 average)
%            Number of connectives :   43 (   0   ~;   2   |;   5   &;  28   @)
%                                         (   1 <=>;   7  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :   15 (   0 sgn;  15   !;   0   ?;   0   ^)
%                                         (  15   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_UNK_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(a_type,type,(
a: \$tType )).

thf(cTHM526_pme,conjecture,(
! [Xr: a > a > \$o,Xx: a,Xy: a] :
( ! [Xq: a > \$o] :
( ( ! [Xw: a] :
( ( ( Xr @ Xx @ Xw )
| ( Xr @ Xw @ Xx ) )
=> ( Xq @ Xw ) )
& ! [Xv: a,Xw: a] :
( ( ( Xq @ Xv )
& ( ( Xr @ Xv @ Xw )
| ( Xr @ Xw @ Xv ) ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy ) )
<=> ! [Xp: a > a > \$o] :
( ( ! [Xx0: a,Xy0: a] :
( ( Xr @ Xx0 @ Xy0 )
=> ( Xp @ Xx0 @ Xy0 ) )
& ! [Xx0: a,Xy0: a] :
( ( Xp @ Xx0 @ Xy0 )
=> ( Xp @ Xy0 @ Xx0 ) )
& ! [Xx0: a,Xy0: a,Xz: a] :
( ( ( Xp @ Xx0 @ Xy0 )
& ( Xp @ Xy0 @ Xz ) )
=> ( Xp @ Xx0 @ Xz ) ) )
=> ( Xp @ Xx @ Xy ) ) ) )).

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