## TPTP Problem File: SEV225^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV225^5 : TPTP v7.5.0. Bugfixed v5.3.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem from REALS-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0676 [Bro09]

% Status   : Theorem
% Rating   : 0.00 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.33 v5.4.0, 0.20 v5.3.0
% Syntax   : Number of formulae    :    6 (   0 unit;   4 type;   1 defn)
%            Number of atoms       :   12 (   2 equality;   4 variable)
%            Maximal formula depth :    7 (   4 average)
%            Number of connectives :    8 (   2   ~;   0   |;   1   &;   4   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4   :;   0   =)
%            Number of variables   :    2 (   0 sgn;   2   !;   0   ?;   0   ^)
%                                         (   2   :;   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
% Bugfixes : v5.2.0 - Added missing type declarations.
%          : v5.3.0 - Fixed tType to \$tType from last bugfixes.
%------------------------------------------------------------------------------
thf(r_type,type,(
r: \$tType )).

thf(c0_type,type,(
c0: r )).

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

thf(cIRREFLEXIVE_LAW_type,type,(
cIRREFLEXIVE_LAW: \$o )).

thf(cIRREFLEXIVE_LAW_def,definition,
( cIRREFLEXIVE_LAW
= ( ! [Xx: r] :
~ ( less @ Xx @ Xx ) ) )).

thf(cPARNAS_FIG3_A,conjecture,
( cIRREFLEXIVE_LAW
=> ! [Xx: r] :
~ ( ( less @ Xx @ c0 )
& ( Xx = c0 ) ) )).

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