## TPTP Problem File: SEV117^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV117^5 : 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_1065 [Bro09]

% Status   : Unknown
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :    5 (   0 unit;   4 type;   0 defn)
%            Number of atoms       :   44 (   0 equality;  34 variable)
%            Maximal formula depth :   13 (   5 average)
%            Number of connectives :   43 (   0   ~;   2   |;   5   &;  28   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4   :;   0   =)
%            Number of variables   :   12 (   0 sgn;  12   !;   0   ?;   0   ^)
%                                         (  12   :;   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(y,type,(
y: a )).

thf(r,type,(
r: a > a > \$o )).

thf(x,type,(
x: a )).

thf(cTHM526_2_pme,conjecture,
( ! [Xp: a > a > \$o] :
( ( ! [Xx0: a,Xy0: a] :
( ( r @ 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 @ x @ y ) )
=> ! [Xq: a > \$o] :
( ( ! [Xw: a] :
( ( ( r @ x @ Xw )
| ( r @ Xw @ x ) )
=> ( Xq @ Xw ) )
& ! [Xv: a,Xw: a] :
( ( ( Xq @ Xv )
& ( ( r @ Xv @ Xw )
| ( r @ Xw @ Xv ) ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ y ) ) )).

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