## TPTP Problem File: SEV146^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV146^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem from TRANSITIVE-CLOSURE
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1133 [Bro09]

% Status   : Theorem
% Rating   : 0.08 v7.4.0, 0.00 v7.3.0, 0.10 v7.2.0, 0.00 v6.2.0, 0.17 v6.0.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.1.0, 0.33 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   59 (   0 equality;  59 variable)
%            Maximal formula depth :   17 (  10 average)
%            Number of connectives :   58 (   0   ~;   0   |;  10   &;  34   @)
%                                         (   0 <=>;  14  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :   22 (   0 sgn;  22   !;   0   ?;   0   ^)
%                                         (  22   :;   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(a_type,type,(
a: \$tType )).

thf(cTHM525_pme,conjecture,(
! [Xr: a > a > \$o] :
( ! [Xx: a,Xy: a] :
( ( Xr @ Xx @ Xy )
=> ! [Xq: a > \$o] :
( ( ! [Xw: a] :
( ( Xr @ Xx @ Xw )
=> ( Xq @ Xw ) )
& ! [Xv: a,Xw: a] :
( ( ( Xq @ Xv )
& ( Xr @ Xv @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy ) ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( ! [Xq: a > \$o] :
( ( ! [Xw: a] :
( ( Xr @ Xx @ Xw )
=> ( Xq @ Xw ) )
& ! [Xv: a,Xw: a] :
( ( ( Xq @ Xv )
& ( Xr @ Xv @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy ) )
& ! [Xq: a > \$o] :
( ( ! [Xw: a] :
( ( Xr @ Xy @ Xw )
=> ( Xq @ Xw ) )
& ! [Xv: a,Xw: a] :
( ( ( Xq @ Xv )
& ( Xr @ Xv @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xz ) ) )
=> ! [Xq: a > \$o] :
( ( ! [Xw: a] :
( ( Xr @ Xx @ Xw )
=> ( Xq @ Xw ) )
& ! [Xv: a,Xw: a] :
( ( ( Xq @ Xv )
& ( Xr @ Xv @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xz ) ) ) ) )).

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