## TPTP Problem File: SEV038^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV038^5 : 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_1210 [Bro09]

% Status   : Unknown
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :  114 (   7 equality; 107 variable)
%            Maximal formula depth :   19 (  10 average)
%            Number of connectives :  101 (   2   ~;   0   |;  27   &;  57   @)
%                                         (   0 <=>;  15  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   27 (  27   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :   38 (   0 sgn;  28   !;  10   ?;   0   ^)
%                                         (  38   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_UNK_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(cTHM266_pme,conjecture,(
? [F: ( ( a > \$o ) > \$o ) > a > a > \$o] :
( ! [P: ( a > \$o ) > \$o] :
( ( ! [Xp: a > \$o] :
( ( P @ Xp )
=> ? [Xz: a] :
( Xp @ Xz ) )
& ! [Xx: a] :
? [Xp: a > \$o] :
( ( P @ Xp )
& ( Xp @ Xx )
& ! [Xq: a > \$o] :
( ( ( P @ Xq )
& ( Xq @ Xx ) )
=> ( Xq = Xp ) ) ) )
=> ( ! [Xx: a] :
( F @ P @ Xx @ Xx )
& ! [Xx: a,Xy: a] :
( ( F @ P @ Xx @ Xy )
=> ( F @ P @ Xy @ Xx ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( ( F @ P @ Xx @ Xy )
& ( F @ P @ Xy @ Xz ) )
=> ( F @ P @ Xx @ Xz ) ) ) )
& ! [R: a > a > \$o] :
( ( ! [Xx: a] :
( R @ Xx @ Xx )
& ! [Xx: a,Xy: a] :
( ( R @ Xx @ Xy )
=> ( R @ Xy @ Xx ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( ( R @ Xx @ Xy )
& ( R @ Xy @ Xz ) )
=> ( R @ Xx @ Xz ) ) )
=> ? [P: ( a > \$o ) > \$o] :
( ! [Xp: a > \$o] :
( ( P @ Xp )
=> ? [Xz: a] :
( Xp @ Xz ) )
& ! [Xx: a] :
? [Xp: a > \$o] :
( ( P @ Xp )
& ( Xp @ Xx )
& ! [Xq: a > \$o] :
( ( ( P @ Xq )
& ( Xq @ Xx ) )
=> ( Xq = Xp ) ) )
& ( R
= ( F @ P ) ) ) )
& ! [T: ( a > \$o ) > \$o,U: ( a > \$o ) > \$o] :
( ( ( T != U )
& ! [Xp: a > \$o] :
( ( T @ Xp )
=> ? [Xz: a] :
( Xp @ Xz ) )
& ! [Xx: a] :
? [Xp: a > \$o] :
( ( T @ Xp )
& ( Xp @ Xx )
& ! [Xq: a > \$o] :
( ( ( T @ Xq )
& ( Xq @ Xx ) )
=> ( Xq = Xp ) ) )
& ! [Xp: a > \$o] :
( ( U @ Xp )
=> ? [Xz: a] :
( Xp @ Xz ) )
& ! [Xx: a] :
? [Xp: a > \$o] :
( ( U @ Xp )
& ( Xp @ Xx )
& ! [Xq: a > \$o] :
( ( ( U @ Xq )
& ( Xq @ Xx ) )
=> ( Xq = Xp ) ) ) )
=> ( ( F @ T )
!= ( F @ U ) ) ) ) )).

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