## TPTP Problem File: SEV319^6.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV319^6 : TPTP v7.5.0. Released v5.1.0.
% Domain   : Set Theory
% Problem  : TPS problem THM145L1
% Version  : Especial.
% English  : Related to the Knaster-Tarski theorem.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0572 [Bro09]
%          : THM145L1 [TPS]

% Status   : Theorem
% Rating   : 0.92 v7.5.0, 1.00 v5.1.0
% Syntax   : Number of formulae    :    3 (   0 unit;   2 type;   0 defn)
%            Number of atoms       :   40 (   0 equality;  30 variable)
%            Maximal formula depth :   12 (   6 average)
%            Number of connectives :   39 (   0   ~;   0   |;   4   &;  28   @)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   2   :;   0   =)
%            Number of variables   :   12 (   0 sgn;  11   !;   1   ?;   0   ^)
%                                         (  12   :;   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
%          : Polymorphic definitions expanded.
%          : Renamed from SEV320^5
%------------------------------------------------------------------------------
thf(a_type,type,(
a: \$tType )).

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

thf(cTHM145L1_pme,conjecture,(
! [U: ( a > \$o ) > a] :
( ( ! [Xx: a,Xy: a,Xz: a] :
( ( ( cLQ @ Xx @ Xy )
& ( cLQ @ Xy @ Xz ) )
=> ( cLQ @ Xx @ Xz ) )
& ! [Xs: a > \$o] :
( ! [Xz: a] :
( ( Xs @ Xz )
=> ( cLQ @ Xz @ ( U @ Xs ) ) )
& ! [Xj: a] :
( ! [Xk: a] :
( ( Xs @ Xk )
=> ( cLQ @ Xk @ Xj ) )
=> ( cLQ @ ( U @ Xs ) @ Xj ) ) ) )
=> ! [Xf: a > a] :
( ! [Xx: a,Xy: a] :
( ( cLQ @ Xx @ Xy )
=> ( cLQ @ ( Xf @ Xx ) @ ( Xf @ Xy ) ) )
=> ? [Xw: a] :
( ( cLQ @ Xw @ ( Xf @ Xw ) )
& ( cLQ @ ( Xf @ Xw ) @ Xw ) ) ) ) )).

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