## TPTP Problem File: SEV023^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV023^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem from EQUIVALENCE-RELATIONS-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1090 [Bro09]

% Status   : Theorem
% Rating   : 0.73 v7.5.0, 1.00 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   40 (   2 equality;  38 variable)
%            Maximal formula depth :   16 (   9 average)
%            Number of connectives :   35 (   0   ~;   0   |;   8   &;  19   @)
%                                         (   1 <=>;   7  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   13 (  13   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :   18 (   0 sgn;  13   !;   4   ?;   1   ^)
%                                         (  18   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_EQU_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(cTHM262_D_EXT_pme,conjecture,
( ! [Xp: a > \$o,Xa: a > \$o] :
( ! [Xb: a] :
( ( Xp @ Xb )
= ( Xa @ Xb ) )
=> ! [P: ( a > \$o ) > \$o] :
( ( P @ Xp )
=> ( P @ Xa ) ) )
=> ! [P: ( a > \$o ) > \$o] :
( ( ! [Xp: a > \$o] :
( ( P @ Xp )
=> ? [Xz: a] :
( Xp @ Xz ) )
& ! [Xx: a] :
? [Xp: a > \$o] :
( ( P @ Xp )
& ( Xp @ Xx ) )
& ! [Xx: a,Xy: a,Xp: a > \$o,Xq: a > \$o] :
( ( ( P @ Xp )
& ( P @ Xq )
& ( Xp @ Xx )
& ( Xq @ Xx )
& ( Xp @ Xy ) )
=> ( Xq @ Xy ) ) )
=> ? [Q: a > a > \$o] :
( ( ^ [Xs: a > \$o] :
( ? [Xz: a] :
( Xs @ Xz )
& ! [Xx: a] :
( ( Xs @ Xx )
=> ! [Xy: a] :
( ( Xs @ Xy )
<=> ( Q @ Xx @ Xy ) ) ) ) )
= P ) ) )).

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