## TPTP Problem File: SEV057^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV057^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem EQP1-1A
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0323 [Bro09]
%          : EQP1-1A [TPS]

% Status   : Theorem
% Rating   : 0.55 v7.5.0, 0.29 v7.4.0, 0.22 v7.2.0, 0.25 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.0.0, 0.14 v5.5.0, 0.33 v5.4.0, 0.40 v4.1.0, 0.33 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   22 (   3 equality;  19 variable)
%            Maximal formula depth :   14 (   8 average)
%            Number of connectives :   15 (   0   ~;   0   |;   4   &;   8   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :    6 (   0 sgn;   4   !;   2   ?;   0   ^)
%                                         (   6   :;   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
%          : Polymorphic definitions expanded.
%------------------------------------------------------------------------------
thf(a_type,type,(
a: \$tType )).

thf(cEQP1_1A_pme,conjecture,(
! [Xx: a > \$o] :
? [Xs: a > a] :
( ! [Xx0: a] :
( ( Xx @ Xx0 )
=> ( Xx @ ( Xs @ Xx0 ) ) )
& ! [Xy: a] :
( ( Xx @ Xy )
=> ? [Xx0: a] :
( ( Xx @ Xx0 )
& ( Xy
= ( Xs @ Xx0 ) )
& ! [Xz: a] :
( ( ( Xx @ Xz )
& ( Xy
= ( Xs @ Xz ) ) )
=> ( Xz = Xx0 ) ) ) ) ) )).

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