## TPTP Problem File: SEV419^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV419^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory
% Problem  : TPS problem from SETS-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1013 [Bro09]

% Status   : Unknown
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :    3 (   0 unit;   2 type;   0 defn)
%            Number of atoms       :   32 (   3 equality;  29 variable)
%            Maximal formula depth :   11 (   5 average)
%            Number of connectives :   25 (   0   ~;   0   |;   2   &;  15   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   2   :;   0   =)
%            Number of variables   :   13 (   0 sgn;  12   !;   1   ?;   0   ^)
%                                         (  13   :;   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(b_type,type,(
b: \$tType )).

thf(cTHM593_pme,conjecture,(
! [F: ( a > \$o ) > b > \$o] :
( ( ! [X: a > \$o,Y: a > \$o] :
( ! [Xx: a] :
( ( X @ Xx )
=> ( Y @ Xx ) )
=> ! [Xx: b] :
( ( F @ X @ Xx )
=> ( F @ Y @ Xx ) ) )
& ! [X: a > \$o,Y: a > \$o] :
( ( ( F @ X )
= ( F @ Y ) )
=> ( X = Y ) )
& ! [Z: b > \$o] :
? [Y: a > \$o] :
( ( F @ Y )
= Z ) )
=> ! [X: a > \$o,Y: a > \$o] :
( ! [Xx: b] :
( ( F @ X @ Xx )
=> ( F @ Y @ Xx ) )
=> ! [Xx: a] :
( ( X @ Xx )
=> ( Y @ Xx ) ) ) ) )).

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