## TPTP Problem File: SEV311^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV311^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem from SET-KNASTER-TARSKI-INST
% Version  : Especial.
% English  : Related to the Knaster-Tarski theorem.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0967 [Bro09]

% Status   : Theorem
% Rating   : 0.17 v7.5.0, 0.25 v7.4.0, 0.22 v7.3.0, 0.20 v7.2.0, 0.25 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.2.0, 0.33 v6.1.0, 0.17 v5.5.0, 0.20 v5.4.0, 0.25 v5.3.0, 0.50 v5.2.0, 0.75 v5.0.0, 0.50 v4.1.0, 1.00 v4.0.0
% Syntax   : Number of formulae    :    3 (   0 unit;   2 type;   0 defn)
%            Number of atoms       :   26 (   0 equality;  21 variable)
%            Maximal formula depth :   13 (   6 average)
%            Number of connectives :   25 (   0   ~;   0   |;   0   &;  16   @)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   2   :;   0   =)
%            Number of variables   :   10 (   0 sgn;   9   !;   0   ?;   1   ^)
%                                         (  10   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_NEQ_NAR

% Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
%            project in the Department of Mathematical Sciences at Carnegie
%          : May require description or choice.
%------------------------------------------------------------------------------
thf(a_type,type,(
a: \$tType )).

thf(cF,type,(
cF: ( a > \$o ) > a > \$o )).

thf(cTHM521_pme,conjecture,
( ! [X: a > \$o,Y: a > \$o] :
( ! [Xx: a] :
( ( X @ Xx )
=> ( Y @ Xx ) )
=> ! [Xx: a] :
( ( cF @ X @ Xx )
=> ( cF @ Y @ Xx ) ) )
=> ! [Xx: a] :
( ( cF
@ ^ [Xx0: a] :
! [S: a > \$o] :
( ! [Xx1: a] :
( ( cF @ S @ Xx1 )
=> ( S @ Xx1 ) )
=> ( S @ Xx0 ) )
@ Xx )
=> ! [S: a > \$o] :
( ! [Xx0: a] :
( ( cF @ S @ Xx0 )
=> ( S @ Xx0 ) )
=> ( S @ Xx ) ) ) )).

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